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This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number ($Re_\tau = 10^4$) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers ($Re_\tau \in [180;10^{10}]$). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future., Comment: arXiv admin note: text overlap with arXiv:2211.03614

The continuum approach employing porous media models is a robust and efficient solution method in the area of the simulation of fixed-bed reactors. This paper applies the double-averaging methodology to refine the continuum approach, opening a way to alleviate its main limitations: space-invariant averaging volume and inaccurate treatment of the porous/fluid interface. The averaging operator is recast as a general space-time filter allowing for the analysis of commutation errors in a classic large eddy simulation (LES) formalism. An explicit filtering framework has been implemented to carry out an a posteriori evaluation of the unclosed terms appearing in the double-averaged Navier-Stokes (DANS) equations, also considering a space-varying filter width. Two resolved simulations have been performed. First, the flow around a single, stationary particle has been used to validate derived equations and the filtering procedure. Second, an LES of the turbulent flow in a channel partly occupied with a porous medium has been realized and filtered. The commutation error at the porous-fluid interface has been evaluated and compared to the prediction of two models. The significance of the commutation error terms is also discussed and assessed. Finally, the solver for DANS equations has been developed and used to simulate both of the studied geometries. The magnitude of the error associated with neglecting the commutation errors has been investigated, and an LES simulation combined with a porous drag model was performed. Very encouraging results have been obtained indicating that the inaccuracy of the drag closure overshadows the error related to the commutation of operators., 52 page, 21 figures

Respirators provide protection from inhalation exposure to dangerous substances, such as chemicals and infectious particles, including SARS-Covid-laden droplets and aerosols. However, they are prone to exposure to stale air as the masks creat a microclimate influenced by the exhaled air. As a result, exhaled air from the lungs accumulating in the mask produce a warm and humid environment that has a high concentration of carbon dioxide (CO2), unsuitable for re-inhalation. Fans are a favourable option for respirators to ventilate the mask and remove the stale air. This study utilized computational fluid dynamics simulation consisting of a hybrid Reynolds-averaged Navier-Stokes (RANS)-large eddy simulation (LES) turbulence method to compare the inhalation flow properties for different fan locations (bottom, top, and side) with regular respirator breathing. Three mask positions, top, side, and bottom, were evaluated under two breathing cycles (approximately 9.65s of breathing time). The results demonstrated that adding a fan respirator significantly decreased internal mask temperature, humidity, and CO2 concentration. The average CO2 concentration decreased by 87%, 67% and 73% for locations bottom, top and side respectively. Whilst the top and side fan locations enhanced the removal of the exhaled gas mixture, the bottom-fan respirator was more efficient in removing the nostril jet gas mixture and therefore provided the least barrier to respiratory function. The results provide valuable insights into the benefits of fan respirators for long-term use for reducing CO2 concentration, mask temperature, and humidity, improving wearer safety and comfort in hazardous environments, especially during the COVID-19 pandemic., 23 Pages, 7 Figures

Density gradients aligned at an angle to pressure gradients result in baroclinic torque in fluid flows, generating vorticity. In this work, we study the vorticity generated by the baroclinic torque exerted by the interaction of pressure jumps across random two-dimensional shock waves with density gradients. A field of random two-dimensional shock waves has acoustic spectral energy scaling as {\epsilon}^{2/3}{\ell}^{-1/3}k^{-2} where k is the wavenumber, {\epsilon} is the energy dissipation, and \ell is the integral length scale of the field. Since the acoustic energy is broadband, pressure and velocity gradients exist in a wide range of length scales. We study the interaction of these broadband gradients with isobaric thermal gradients localized at a length scale in the spectral space. We show that the method of generating shock waves or injection of wave energy in the system governs the baroclinic interactions. For stochastically forced shock waves, baroclinic termsare negligible. Broadband vorticity with energy at least two orders of magnitude smaller is generated due to continuous variation in curvature of shock waves caused by stochastic forcing. On the other hand, shock waves maintained by energy rescaling result in the generation of coherent vorticity. We also discuss the relative magnitude of the baroclinic torque generated due to total density gradients compared to the one generated due to non-isentropic density gradients within the shock waves interacting with the pressure gradients.

In the last decade, with the growing demand for efficient and more sustainable products that reduce our CO2 footprint, progresses in Additive Manufacturing (AM) have paved the way for optimized heat exchangers, whose disruptive design will heavily depend on predictive numerical simulations. Typical AM rough surfaces show limited resemblance to the artificially constructed rough surfaces that have been the basis of most prior fundamental research on turbulent flow over rough walls. Hence, current wall models used in steady and unsteady three-dimensional (3D) Navier–Stokes simulations do not consider such characteristics. Therefore, a high-fidelity Large Eddy Simulation (LES) database is built to develop and assess novel wall models for AM. This article investigates the flow in rough pipes built from the surfaces created using AM techniques at Siemens based on Nickel Alloy IN939 material. We developed a code to generate the desired rough pipes from scanned planar surfaces. We performed high-fidelity LES of turbulent rough pipe flows at Reynolds number, Re = 11 700, to reveal the influence of roughness parameters on turbulence, mainly the average roughness height and the effective slope. The equivalent sand-grain roughnesses, ks, of the present AM rough surfaces are predicted using the Colebrook correlation. The main contributors to the skin friction coefficient are found to be turbulence and drag forces. In the present study, the existence of a logarithmic layer is marked even for high values of ks. The mean flow, the velocity fluctuations, and the Reynolds shear stresses show turbulence's strong dependence on the roughness topography. Profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as zero-plane displacement. The effective distance collapses the shear stresses and the velocity fluctuations outside the roughness sublayer; thus, Townsend's similarity of the streamwise mean velocity is marked for the present roughnesses. Furthermore, a mixed scaling is introduced to improve the collapse of turbulence statistics in the roughness sublayer. In addition, an attempt to investigate the impact of surface roughness on flow physics using the acquired LES results based on quadrant analysis of the Reynolds shear stresses and anisotropy of turbulence is made.

An alternative to the well-known complete form of the Mie-Gr\"uneisen equation of state (EOS) for water is suggested. A closed analytical description of the self-consistent EOS for an arbitrary medium based only on the first law of thermodynamics and on a new form of virial theorem is obtained. This form of the virial theorem (allowing a variable power-law exponent of the particles interaction potential) is a result of the generalization of the known method of similarity (Feynman et al., 1949). In the new EOS, the description of the internal potential energy as a solution of a nonlinear Riemann-Hopf type equation is proposed., Comment: 37 pages, 5 figures

Under the condition of partial surface wettability, thin liquid films can be destabilized by small perturbations and rupture into droplets. As successfully predicted by the thin film equation (TFE), the rupture dynamics are dictated by the liquid–solid interaction. The theory describes the latter using the disjoining pressure or, equivalently, the contact angle. The introduction of a secondary fluid can lead to a richer phenomenology, thanks to the presence of different fluid/surface interaction energies but has so far not been investigated. In this work, we study the rupture of liquid films with different heights immersed in a secondary fluid using a multi-component lattice Boltzmann (LB) approach. We investigate a wide range of surface interaction energies, equilibrium contact angles, and film thicknesses. We found that the rupture time can differ by about one order of magnitude for identical equilibrium contact angles but different surface free energies. Interestingly, the TFE describes the observed breakup dynamics qualitatively well, up to equilibrium contact angles as large as 130°. A small film thickness is a much stricter requirement for the validity of the TFE, and agreement with LB results is found only for ratios [Formula: see text] of the film height h and lateral system size L, such as [Formula: see text].

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate droplet size but fails to approximate droplet shape. This is due to a highly non-linear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont using asymptotic analysis. This asymptotic approach to the Navier-Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference and finite element method. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation (PETSc). The code is verified using the Method of Manufactured Solutions (MMS) and validated using previous experimental studies done by Zhang and Basaran. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena., 11 pages, 6 figures, published in Physics of Fluids

We report a pore-scale numerical study of salt finger convection in porous media, with a focus on the influence of the porosity in the non-Darcy regime, which has received little attention in previous research. The numerical model is based on the lattice Boltzmann method with a multiple-relaxation-time scheme and employs an immersed boundary method to describe the fluid–solid interaction. The simulations are conducted in a two-dimensional, horizontally periodic domain with an aspect ratio of 4, and the porosity [Formula: see text] is varied from 0.7 to 1, while the solute Rayleigh number [Formula: see text] ranges from [Formula: see text] to [Formula: see text]. Our results show that, for all explored [Formula: see text], solute transport first enhances unexpectedly with decreasing [Formula: see text] and then decreases when [Formula: see text] is smaller than a [Formula: see text]-dependent value. On the other hand, while the flow strength decreases significantly as [Formula: see text] decreases at low [Formula: see text], it varies weakly with decreasing [Formula: see text] at high [Formula: see text] and even increases counterintuitively for some porosities at moderate [Formula: see text]. Detailed analysis of the salinity and velocity fields reveals that the fingered structures are blocked by the porous structure and can even be destroyed when their widths are larger than the pore scale, but become more ordered and coherent with the presence of porous media. This combination of opposing effects explains the complex porosity dependencies of solute transport and flow strength. The influence of porous structure arrangement is also examined, with stronger effects observed for smaller [Formula: see text] and higher [Formula: see text]. These findings have important implications for passive control of mass/solute transport in engineering applications.

We develop a moment method based on the Hermite series of the arbitrary order to calculate viscous-slip, thermal-slip, and temperature-jump coefficients for general gas-surface scattering kernels. Under some usual assumptions of scattering kernels, the solvability is obtained by showing the positive definiteness of the symmetric coefficient matrix in the boundary conditions. For gas flows with the Cercignani–Lampis gas–surface interaction and inverse-power-law intermolecular potentials, the model can capture the slip and jump coefficients accurately with elegant analytic expressions. On the one hand, the proposed method can apply to the cases of arbitrary order moments with increasing accuracy. On the other hand, the explicit formulas for low-order situations are simpler and more accurate than some existing results in references. Therefore, one may apply these formulas in slip and jump conditions to improve the accuracy of macroscopic fluid dynamic models for gas flows.

In this short Letter, the structure of a rotating detonation wave (RDW) fueled by biofuel is revealed and expounded. A simulation is carried out under an Eulerian–Lagrangian framework in which the main characteristics of the two-phase RDW are analyzed in detail. The results suggest that a self-sustained rotating detonation fueled by liquid ethanol and air can be achieved with hydrogen addition for combustion enhancement, and a laminated dual-front structure of the RDW due to the effect of droplet evaporation is captured and clarified.

This work focuses on the large eddy simulation and the study of turbulent dilute methanol spray flames in vitiated coflow using the secondary-oxidizer Flamelet Generated Model (FGM). The modified FGM model uses an additional secondary oxidizer parameter in addition to the three other parameters previously used for spray flames—progress variable, mixture fraction, and enthalpy. The results for gas phase and droplet properties are validated against the dilute methanol spray flame database for varying fuel injection amounts. The droplet statistics and the liftoff flame heights are accurately captured for all the cases. A proper orthogonal decomposition (POD) of the scalar fluctuating hydroxyl radical (OH) field and the velocity–temperature field captures the flame structures in the downstream region of ignition kernels. The detailed POD analysis reveals that the base frequency of the dominant OH field equals that of the dominant vortical structure of 67.3 Hz. The flame propagation happens around these dominant vortical structures because of the less-strained fluid mixing.

The interactions between an incident shock and a moderately dense particle curtain are simulated with the Eulerian–Lagrangian method. A customized solver based on OpenFOAM is extended with an improved drag model and collision model and then validated against two benchmark experiments. The results show that the collision model has a limited impact on curtain morphology compared with the improved drag model. In this work, parametric studies are performed considering different particle sizes, volume fractions, and curtain thicknesses. Smaller particle sizes and larger volume fractions lead to stronger reflected shock and weaker transmitted shock. Attention is paid to the particle collision effects on the curtain evolution behaviors. According to our results, for the mono-dispersed particle curtain, the collision effects on curtain front behaviors are small, even when the initial particle volume fraction is as high as 20%. This is due to the positive velocity gradient across the curtain after the shock wave passage, leading to the faster motion of downstream particles than the upstream ones, and hence, no collision occurs. For the bi-dispersed particle curtain, the collision effects become important in the mixing region of different-size particles. Collisions decelerate small particles while accelerating large ones and cause velocity scattering. Moreover, increasing the bi-dispersed curtain thickness leads to multiple collision force peaks, which is the result of the delayed separation of different particle groups. Our results indicate that the collision model may be unnecessary to predict curtain fronts in mono-dispersed particles, but in bi-dispersed particles, the collision effects are important and, therefore, must be modeled.

The elliptical instability is an instability of elliptical streamlines, which can be excited by large-scale tidal flows in rotating fluid bodies, and excites inertial waves if the dimensionless tidal amplitude ($\epsilon$) is sufficiently large. It operates in convection zones but its interactions with turbulent convection have not been studied in this context. We perform an extensive suite of Cartesian hydrodynamical simulations in wide boxes to explore the interactions of the elliptical instability and Rayleigh-B\'enard convection. We find that geostrophic vortices generated by the elliptical instability dominate the flow, with energies far exceeding those of the inertial waves. Furthermore, we find that the elliptical instability can operate with convection, but it is suppressed for sufficiently strong convection, primarily by convectively-driven large-scale vortices. We examine the flow in Fourier space, allowing us to determine the energetically dominant frequencies and wavenumbers. We find that power primarily concentrates in geostrophic vortices, in wavenumbers that are convectively unstable, and along the inertial wave dispersion relation, even in non-elliptically deformed convective flows. Examining linear growth rates on a convective background, we find that convective large-scale vortices suppress the elliptical instability in the same way as the geostrophic vortices created by the elliptical instability itself. Finally, convective motions act as an effective viscosity on large-scale tidal flows, providing a sustained energy transfer (scaling as $\epsilon^2$). Furthermore, we find that the energy transfer resulting from bursts of elliptical instability, when it operates, is consistent with the $\epsilon^3$ scaling found in prior work., Comment: 24 pages, 22 figures, 1 table, accepted for publication in Physics of Fluids

This study presents a detailed investigation of how the rheological behaviour of fluid could influence the electrokinetic instability (EKI) phenomenon in a microfluidic T-junction. The non-Newtonian power-law model with different values of the power-law index (n) is used to obtain fluids of different rheological behaviours. We find that as the fluid rheological behaviour changes from shear-thickening (n > 1) to shear-thinning (n < 1) via the Newtonian (n = 1) one, the EKI phenomenon is significantly influenced under the same conditions. In particular, the intensity of this EKI phenomenon is found to be significantly higher in shear-thinning fluids than in Newtonian and shear-thickening fluids. As a result, the corresponding mixing phenomenon, often achieved using this EKI phenomenon, is also notably enhanced in shear-thinning fluids compared to that achieved in Newtonian and shear-thickening fluids. A detailed analysis of both the flow dynamics and mixing phenomena in terms of streamlines, velocity fluctuations, concentration field, mixing efficiency, etc., is presented and discussed in this study. We also employ the data-driven dynamic mode decomposition (DMD) technique to analyze the flow field in more detail. In particular, the information on the coherent flow structures obtained with different values of the power-law index facilitates the understanding of both the EKI-induced chaotic convection and mixing phenomena in a better way; for instance, why the mixing efficiency is higher in shear-thinning fluids than that in Newtonian and shear-thickening fluids. Moreover, we observe that the spatial expanse and intensity of these coherent structures differ significantly as the power-law index changes, thereby providing valuable insights into certain aspects of the underlying flow dynamics that otherwise are not clearly apparent from other analyses., arXiv admin note: text overlap with arXiv:2205.08735

Control surface deployment in a supersonic flow has many applications, including flow control, mixing, and body-force regulation. The extent of control surface deflections introduces varying flow unsteadiness. The resulting fluid dynamics influence the downstream flow characteristics and fluid-structure interactions severely. In order to understand the gas dynamics, an axisymmetric cylindrical body with a sharp-tip cone at zero angles of attack ($\alpha=0^\circ$) is examined in a free stream Mach number of $M_\infty=2.0$ and Reynolds number of $Re_{D}=2.16 \times 10^6$ ($D=50$ mm). Four static control surface deflection angles ($\theta = \pi/36,\pi/6,\pi/3,\pi/2$, rad) are considered around the base body. The cases are computationally investigated through a commercial flow solver adopting a two-dimensional detached eddy simulation (DES) strategy. Recirculation bubble length, drag coefficient's variation, wall-static pressure statistics, acoustic loading on the model and the surroundings, $x-t$ trajectory and $x-f$ spectral analysis, pressure fluctuation's correlation coefficient on the model, and modal analysis are obtained to understand the flow unsteadiness. At $\theta = [\pi/36]$, the wall-static pressure fluctuations behind the control surface are minimal and periodic, with a mere acoustic load of about 50 dB. At $\theta = [\pi/2]$, a violent periodic fluctuation erupted everywhere around the control surface, leading to a higher acoustic load of about 150 dB (3 times higher than the previous). For $\theta = [\pi/6]$ and $[\pi/3]$, high-frequency fluctuations with small and large-scale structures continuously shed along the reattaching shear layer, thereby causing a broadened spectra in the control surface wake., Comment: 17 Figures. Relevant multimedia views and supplementary videos are embedded in the pdf itself. The article is yet to be submitted to a journal

The effect of buoyant forces on viscous coarsening is studied numerically. It is shown that at any time buoyant forces induce a vertical flow that scales like the Stokes velocity. This does no induce any noticeable change in the morphology of the coarsening microstructure under a value of the characteristic length of the pattern. Above this threshold the pattern evolves toward a quasi two D pattern and coarsening stops. The characteristic length is shown to scale like $\sqrt{\gamma/(g \Delta\rho)}$ where $\gamma$ is he surface tension and $\Delta\rho$ the mass dnsiy difference between the phases., Comment: The following article has been submitted to/accepted by Physics of Fluids. After it is published, it will be found at https://aip.scitation.org/journal/phf

The Boltzmann equation becomes invalid as the size of gas molecules is comparable with the average intermolecular distance. A better description is provided by the Enskog collision operator, which takes into account the finite size of gas molecules. This extension implies non-local collisions as well as an increase in collision frequency, making it computationally expensive to solve. An approximation of the Enskog collision operator, denoted the simplified Enskog collision operator, is used in this work to develop a quadrature-based Lattice Boltzmann model for non-ideal monatomic dense gases. The Shakhov collision term is implemented in order to fine-tune the Prandtl number. This kinetic model is shown to be able to tackle non-equilibrium flow problems of dense gases, namely the sound wave and the shock wave propagation. The results are compared systematically with the results of the more accurate but computationally intensive particle method of solving the Enskog equation. The model introduced in this paper is shown to have good accuracy for small to moderate denseness of the fluid (defined as the ratio of the molecular diameter to the mean free path) and, due to the efficiency in terms of the computational time, it is suitable for practical applications., 16 pages, 8 figures

Accurate and computationally accessible models of liquid film flows allow for optimizing coating processes, such as hot-dip galvanization and vertical slot-die coating. This paper extends a classic three-dimensional integral boundary layer model for falling liquid films (FFs) to account for a moving substrate (MS). We analyze the stability of the liquid films on vertically moving substrates in a linear and in a nonlinear setting. In the linear analysis, we derive the dispersion relation and the temporal growth rates of an infinitesimal disturbance using normal modes and linearized governing equations. In the nonlinear analysis, we consider disturbances of finite size and numerically compute their evolution using the set of nonlinear equations in which surface tension has been removed. We present the region of (linear) stability of both FF and MS configurations, and we place the operating conditions of an industrial galvanizing line in these maps. A wide range of flow conditions was analyzed and shown to be stable according to linear and nonlinear stability analyses. Moreover, the nonlinear analysis, carried out in the absence of surface tension, reveals a nonlinear stabilizing mechanism for the interface dynamics of a liquid film dragged by an upward-moving substrate.

Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invades a quiescent region, and the velocity and pressure in its immediate wake become unbounded at time of collapse. However, these solutions are of border-line physicality: the pressure vanishes within the quiescent region due to vanishing temperature there. It is reasonable that the lack of upstream counter-pressure is conducive to large speeds, with concomitant large amplitudes. Based on Guderley's original solutions it is therefore unclear if it is the zero-pressure region that is responsible for blowup. The same applies to self-similar Euler flows describing radial cavity flow, first analyzed by Hunter (1960). Recent works have shown that the simplified isothermal and isentropic models admit continuous blowup solutions in the presence of a strictly positive pressure field. In this work we extend this conclusion to the case of the full Euler system. The solutions under consideration are radial self-similar flows in which a continuous wave focuses and blows up. We propagate the solutions beyond blowup and observe numerically that there are cases where an expanding spherical shock wave is generated at collapse. The resulting solution has the unusual property that the flow is isentropic in each of the two regions separated by the shock. We finally verify that these are admissible global weak solutions to the full, multi-d compressible Euler system., 19 pages, 2 figures

We study experimentally and numerically the onset of tip streaming in an electrified droplet. The experiments show that, for a sufficiently small dimensionless conductivity, the droplet apex oscillates before ejecting a liquid jet. This effect is caused by the limited charge transfer from the bulk to the interface. This reduces the electrostatic pressure at the droplet's stretching tip, preventing liquid ejection. This reduction of electrostatic pressure is compensated for by the electric shear stress arising during the apex oscillations, which eventually leads to the jet formation. The stability limit calculated from the global stability analysis perfectly agrees with the experimental results. However, this analysis predicts non-oscillatory, non-localized instability in all the cases, suggesting that both the oscillatory behavior and the small local scale characterizing tip streaming arise during the nonlinear droplet deformation., 8 pages, 12 figures

In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature in our inertial flow model behave unrealistically. The goal of the current work is to demonstrate technical possibility of modeling compressible, turbulent flow at low Mach number where both density and temperature behave in a more realistic fashion. Here we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible and inertial flow. Similarly to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically., 20 pages, 8 figures

The properties of rotating turbulence driven by precession are studied using direct numerical simulations and analysis of the underlying dynamical processes in Fourier space. The study is carried out in the local rotating coordinate frame, where precession gives rise to a background shear flow, which becomes linearly unstable and breaks down into turbulence. We observe that this precession-driven turbulence is in general characterized by coexisting two dimensional (2D) columnar vortices and three dimensional (3D) inertial waves, whose relative energies depend on the precession parameter $Po$. The vortices resemble the typical condensates of geostrophic turbulence, are aligned along the rotation axis (with zero wavenumber in this direction, $k_z=0$) and are fed by the 3D waves through nonlinear transfer of energy, while the waves (with $k_z\neq0$) in turn are directly fed by the precessional instability of the background flow. The vortices themselves undergo inverse cascade of energy and exhibit anisotropy in Fourier space. For small $Po0.1$ turbulence is quasi-steady with only mild fluctuations, the coexisting columnar vortices and waves in this state give rise to a split (simultaneous inverse and forward) cascade. Increasing the precession magnitude causes a reinforcement of waves relative to vortices with the energy spectrum approaching Kolmogorov scaling and, therefore, the precession mechanism counteracts the effects of the rotation., 20 pages, 16 figures, 1 table, submitted to Physics of Fluids

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.

Introducing a fluid microjet into the boundary layer to increase fluid momentum and hence delay separation is a method for actively controlling a flow separation region. The present work numerically analyzed the control of a separation bubble behind a ramp. For this purpose, we first verified the numerical results for a flow (without a jet) over the ramp against reliable experimental studies from the literature. Next, the effects of introducing a microjet to the flow were also verified. A jet was then placed at three different distances above the ramp to study its impact on various parameters, including velocities, Reynolds stresses, pressure, vorticity, streamlines, and the separation bubble size. As the jet was moved further back, the jet-induced upwash region grew considerably. Finally, the effects of using three identical jets were studied and compared against those of a single jet. The results indicated that using a three-jet array shrank the separation bubble. Using an array with d/D = 15 can limit laterally the separation bubble about 2.75 times smaller than a single jet in the z-direction. Also, the employment of the jet managed to decrease the length of the separation zone in the x-direction up to 78%, in the case of Lx/L1 = 0.0143 and d/D = 10., Comment: 31 pages, 23 figures, and 1 table

We further elaborate on the generalized formulation for cubic equation of state proposed by Cismondi and Mollerup [Fluid Phase Equilib. 232 (2005)]. With this formulation all well-known cubic equations of state can be described with a certain pair of values, which allows for a generic implementation of different equations of state. Based on this generalized formulation, we derive a complete thermodynamic model for computational fluid dynamics (CFD) simulations by providing the resulting correlations for all required thermodynamic properties. For the transport properties, we employ the Chung correlations. Our generic implementation includes the often used equations of state Soave-Redlich-Kwong and Peng-Robinson and the Redlich-Kwong-Peng-Robinson (RKPR) equation of state. The first two assume a universal compressibility factor and are therefore only suitable for fluids with a matching critical compressibility. The Redlich-Kwong-Peng-Robinson overcomes this limitation by considering the equation of state parameter as function of the critical compressibility. We compare the resulting thermodynamic modeling for the three equations of state for selected fluids with each other and CoolProp reference data. As supplementary material to this paper, we provide a Python tool called real gas thermodynamic python library (realtpl). This tool can be used to evaluate and compare the results for a wide range of different fluids. Additionally, we also provide the implementation of the generalized form in OpenFOAM.

The motion of three-phase contact lines is one of the most relevant research topics of micro- and nano-fluidics. According to many hydrodynamic and molecular models, the dynamics of contact lines is assumed overdamped and dominated by localised liquid-solid friction, entailing the existence of a mobility relation between contact line speed and microscopic contact angle. We present and discuss a set of non-equilibrium atomistic Molecular Dynamics simulations of water nanodroplets spreading on or confined between silica-like walls, showing the existence of the aforementioned relation and its invariance under wetting modes (`spontaneous' or `forced'). Upon changing the wettability of the walls, it has been noticed that more hydrophilic substrates are easier to wet rather than de-wet; we show how this asymmetry can be automatically captured by a contact line friction model that accounts for the molecular transport between liquid layers. A simple examination of the order and orientation of near-contact-line water molecules corroborates the physical foundation of the model. Lastly, we propose an approach to discriminate between contact line friction models which overcomes the limitations of experimental resolution. This work constitutes a stepping stone towards demystifying wetting dynamics on high-friction hydrophilic substrates and underlines the relevance of contact line friction in modelling the motion of three-phase contact lines., 11 pages (double column), 11 figures, submitted to Physics of Fluids

Weakly ionized plasmas, formed in high enthalpy hypersonic flows, can be actively manipulated via imposed magnetic fields—a concept termed magnetohydrodynamic (MHD) flow control. Imposed MHD effects, within flows that exhibit multiple shock interactions, are consequential for emerging aerospace technologies, including the possibility of replacing mechanical control surfaces with magnetic actuation. However, numerical modeling of this flow type remains challenging due to the sensitivity of feature formation and the real gas modeling of weakly ionized, electrically conductive, air plasma. In this work, numerical simulation capabilities have been developed for the study of MHD affected, hypersonic flows, around two-dimensional axisymmetric non-simple geometries. The validated numerical methodology, combined with an advanced 19 species equation of state for air plasma, permits the realistic and efficient simulation of air plasmas in the equilibrium regime. Quantitative agreement is achieved between simulation and experiment for a Mach 5.6 double cone geometry with applied magnetic field. In the context of the magnetic actuation concept, numerical studies are conducted for varied conical surface angle and magnetic field configuration. For simple geometries with an elemental shock type, the MHD enhancement effect produces a self-similar shock structure. This paper demonstrates how, for hypersonic flows with complex shock interactions, the MHD affected flow is not only augmented in terms of shock position but may exhibit topological adaptations in the fundamental flow structure. A classification system is introduced for the emergent flow topologies identified in this work. Fluid-magnetic interactions are explored and explained in terms of the coupled mechanisms leading to (1) differences in magnitude of MHD enhancement effect and (2) structural adaptations of the flow topology. The applied numerical studies examine why increased conical surface angle does not amplify the MHD enhancement effect as expected from the base flow conditions, and the mechanisms by which the magnetic field configuration influences the MHD augmented shock structure. Most critically, classes of conditions are identified that produce topological equivalence between the magnetic interaction effects and a generalized mechanical control surface.

We present physics-based nozzle design rules to achieve high-throughput and stable jetting in drop-on-demand liquid metal 3D printing. The design rules are based on scaling laws that capture the change of meniscus oscillation relaxation time with geometric characteristics of the nozzle's inner profile. These characteristics include volume, cross-sectional area, and inner surface area of the nozzle. Using boundary layer theory for a simple geometry, we show that the meniscus settles faster when the ratio of inner surface area to volume is increased. High-fidelity multiphase flow simulations verify this scaling. We use these laws to explore several design concepts with parameterized classes of shapes that reduce the meniscus relaxation time while preserving desired droplet specs. Finally, we show that for various nozzle profile concepts, the optimal performance can be achieved by increasing the ratio of the circumferential surface area to the bulk volume to the extent that is allowable by manufacturing constraints., Comment: Under Review in Physics of Fluids, AIP Publishing

We present a user-friendly open-source MATLAB\textsuperscript{\textregistered} package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg. Firstly, this package helps the user to perform a very basic statistical analysis of a given turbulent data set which we believe to be useful to the entire turbulence community. It can be used to estimate the statistical quantities of turbulence such as the spectrum density, turbulent intensity, integral length scale, Taylor microscale, Kolmogorov scale and dissipation rate. Different well-known methods available in the literature were selected so that they can be compared. Secondly, this package also performs an advanced analysis which includes the scale-dependent statistical description of turbulent cascade using the Fokker-Planck equation which consequently leads to the assessment of integral fluctuation theorem. This is utilized to estimate velocity increments, structure functions and their scaling exponents, drift and diffusion coefficients of the Fokker-Planck equation and consequently the total entropy production of the turbulent cascade. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. The knowledge of a Fokker-Planck equation allows to determine for each independent cascade trajectories a total entropy production. The estimation of total entropy production allows to verify a rigorous law of non-equilibrium stochastic thermodynamics, namely the integral fluctuation theorem, which must be valid if Markov properties hold and the Fokker-Planck equation is correct. This approach to the turbulent cascade process has the potential for a new way to link the statistical description of turbulence, non-equilibrium stochastic thermodynamics and local turbulent flow structures., This open source MATLAB package can be downloaded with all the supplementary material (data, source code and standalone applications (64-bit) for Windows, macOS and Linux) to replicate all the results presented in this paper from the repository on GitHub https://github.com/andre-fuchs-uni-oldenburg/OPEN_FPE_IFT

The contact angle between a gas–liquid interface and a solid surface is a function of the dynamic conditions of the contact line. Classic steady correlations link the contact angle to the contact line velocity. However, it is unclear whether they hold in the presence of inertia and the case of perfect wetting fluids. We analyze by means of experiments the shape of a liquid interface and the corresponding contact angle in accelerating conditions for two different fluids, that is, HFE7200 (perfect wetting) and demineralized water. The setup consists of a U-shaped quasi-capillary tube in which the liquid column oscillates in response to a pressure step on one of the two sides. We obtained the evolution of the interface shape from high-speed back-light visualization, fit interface models to the experimental data to estimate the contributions of all the governing forces, and perform measurements of the dynamic contact angle. We propose a new model to account for the impact of the interface acceleration on its shape, and we discuss the impact on the measurement of the transient contact angle. The new model allows us to perform dynamic contact angle measurements below 15°, which is challenging to obtain with traditional techniques. We show for the first time a dynamic characterization of the wetting behavior of HFE7200, and we compare the results with traditional hydrodynamic models.

This article aims to make a detailed analysis of co-flowing plane Couette flows. Particularly, the variation of flow quantities from the turbulent to non-turbulent region is studied. While the enstrophy exhibits a sharp jump, the other quantities (e.g., mean velocity, Reynolds normal stress, and kinetic energy) show a continuous variation across the interface. The budget analysis of Reynolds normal stresses reveals that the terms playing a key role in turbulence transportation vary depending on the Reynolds normal stress under study. The terms production, diffusion, and redistribution play an important role in streamwise Reynolds stress {\dh}u0u0 {\TH}. In the spanwise Reynolds stress {\dh}v0v0 {\TH}, the diffusion terms play a significant role. In the wall-normal Reynolds stress {\dh}w0w0 {\TH}, only the redistribution term is significant. The influence of one flow over another in the co-flow state was observed through the additional mean velocity and Reynolds normal stress found in the system compared to a standard plane Couette flow (pCf). Comparing the co-flow system with a conventional pCf system, the former exhibits greater vorticity, vortex stretching, and kinetic energy. A detailed analysis on the geometry and topology of flow structures was studied using flow invariants., Comment: 17 PAGES, 21 FIGURES

This work considers the gravitational instability of a saline boundary layer formed by an evaporation-induced flow through a fully-saturated porous slab. Evaporation of saline waters can eventually result in the formation of salt lakes as salt accumulates. As natural convection can impede the accumulation of salt, establishing a relation between its occurrence and the value of physical parameters such as evaporation rate, height of the slab or porosity is crucial. One step towards determining when gravitational instabilities can arise is to compute the ground-state salinity, that evolves due to the uniform upwards flow caused by evaporation. The resulting salt concentration profile exhibits a sharply increasing salt concentration near the surface, which can lead to a gravitationally unstable setting. In this work, this ground state is analytically derived within the framework of Sturm-Liouville theory. Then, the method of linear stability in conjunction with the quasi-steady state approach is employed to investigate the occurrence of instabilities. These instabilities can develop and grow over time depending on the Rayleigh number and the dimensionless height of the porous medium. To calculate the critical Rayleigh number, which can determine the stability of a particular system, the eigenvalues of the linear perturbation equations have to be computed. Here, a novel fundamental matrix method is proposed to solve this eigenvalue problem and shown to coincide with an established Chebyshev-Galerkin method in their shared range of applicability. Finally, a 2-dimensional direct numerical simulation of the full equation system via the finite volume method is employed to validate the time of onset of convective instabilities predicted by the linear theory. Moreover, the fully nonlinear convection patterns are analyzed.

The unsteady motion of a gas–liquid interface, such as during splashing or atomization, often results in complex liquid structures embedded in the ambient fluid. Here, we explore the use of skeletonization to identify the minimum amount of information needed to describe their geometry. We skeletonize a periodic liquid jet by a modification of a recently introduced approach to coarsen multiphase flows while retaining a sharp interface. The process consists of diffusing an index function and at the same time moving the interfaces with it, until they “collapse” into each other and form skeletons. The skeleton represents the basic topology of the jet and we also keep track of how much the interface is moved (or how much volume is “accumulated”) during the process, which can be used to approximately reconstruct the jet. We explore various quantitative measures to characterize and distinguish the skeletons. These include standard morphometrics such as branch length distribution, after segmenting the skeletons into branches, and a more sophisticated representation of the skeleton structures called topology morphology descriptor, to obtain an “equivalent” description of the skeletons by retaining information about the topology in a compact way.

Coalescence of two droplets on a solid substrate is an interfacial phenomenon that imposes the challenges of capturing the complex contact line motion and energy interaction between the solid–liquid interface. Recent investigations on the coalescence of polymeric droplets on a solid substrate have reported strong disagreements; the heart of the issue is whether coalescence of polymeric drops is similar to that of Newtonian fluid and is independent of molecular relaxation, or whether the role of entanglement of polymeric chains leads to a transition kinetics different from that of Newtonian fluid. Via this article, we resolve the disagreements through a discussion on the effects of merging method on the dominant forces governing the coalescence process, i.e., inertia, dissipation, and relaxation. In this regard, two methods of merging have been identified, namely, the droplet spreading method and the volume filling method. Our study unveils that the coalescence dynamics of polymeric drops is not universal and, in fact, is contingent of the method by which the coalescence is triggered. Additionally, we demonstrate the spatial features of the bridge at different time instants by a similarity analysis. We also theoretically obtain a universal bridge profile by employing the similarity parameter in a modified thin film lubrication equation for polymeric fluids.

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well with the previous numerical and experimental results. In these simulations, the density ratio and the Reynolds number can reach a large value of [Formula: see text]. Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.

Relative permeability is commonly used to model immiscible fluid flow through porous materials. In this work, we derive the relative permeability relationship from conservation of energy, assuming that the system to be non-ergodic at large length scales and relying on averaging in both space and time to homogenize the behavior. Explicit criteria are obtained to define stationary conditions: (1) there can be no net change for extensive measures of the system state over the time averaging interval; (2) the net energy inputs into the system are zero, meaning that the net rate of work done on the system must balance with the heat removed; and (3) there is no net work performed due to the contribution of internal energy fluctuations. Results are then evaluated based on direct numerical simulation. Dynamic connectivity is observed during steady-state flow, which is quantitatively assessed based the Euler characteristic. We show that even during steady-state flow at low capillary number ([Formula: see text]), typical flow processes will explore multiple connectivity states. The residence time for each connectivity state is captured based on the time-and-space average. The distribution for energy fluctuations is shown to be multi-modal and non-Gaussian when terms are considered independently. However, we demonstrate that their sum is zero. Given an appropriate choice of the thermodynamic driving force, we show that the conventional relative permeability relationship is sufficient to model the energy dissipation in systems with complex pore-scale dynamics that routinely alter the structure of fluid connected pathways.

Similarity laws of aerodynamics are of crucial importance in both pre-computer time and the modern era, since they can greatly facilitate relevant aerodynamic analyses, wind tunnel experiments, and aircraft designs. In this Letter, we present a new similarity law for steady transonic–supersonic flow over thin bodies at a small angle of attack. The new similarity law is based on the extrapolation of the lift and drag coefficient slopes at a sonic point, which are obtained from the single longitudinal process. The effect of transverse process on the drag coefficient is accounted for afterwards by introducing a dimensionless wake width, which can be theoretically estimated. The remarkable feature of the new similarity law is that it depends on both the free-stream Mach number and the specific heat ratio. The validity of the new similarity law is confirmed by the excellent agreement with numerical data of the flow over a two-dimensional airfoil with the free-stream Mach number between 0.9 and 2.

When two fluids of different electrical conductivities are transported side by side in a microfluidic device under the influence of an electric field, an electrokinetic instability (EKI) is often generated after some critical values of the applied electric field strength and conductivity ratio. Many prior experimental and numerical studies show that this phenomenon results in a chaotic flow field inside a microdevice, thereby facilitating the mixing of two fluids if they are Newtonian in behavior. However, the present numerical study shows that this chaotic convection arising due to the electrokinetic instability can be suppressed if the fluids are viscoelastic instead of Newtonian ones. In particular, we observe that as the Weissenberg number (ratio of the elastic to that of the viscous forces) gradually increases and the polymer viscosity ratio (ratio of the solvent viscosity to that of the zero-shear rate viscosity of the polymeric solution) gradually decreases, the chaotic fluctuation inside a T microfluidic junction decreases within the present range of conditions encompassed in this study. We demonstrate that this suppression of the chaotic motion occurs due to the formation of a strand of high elastic stresses at the interface of the two fluids. We further show that this suppression of the chaotic fluctuation (particularly, the span-wise one) inhibits the mixing of two viscoelastic fluids. Therefore, one needs to be cautious when the EKI phenomenon is planned to use for mixing such viscoelastic fluids. Our observations are in line with that seen in limited experimental studies conducted for these kinds of viscoelastic fluids.

We propose an open-source Python platform for applications of deep reinforcement learning (DRL) in fluid mechanics. DRL has been widely used in optimizing decision making in nonlinear and high-dimensional problems. Here, an agent maximizes a cumulative reward by learning a feedback policy by acting in an environment. In control theory terms, the cumulative reward would correspond to the cost function, the agent to the actuator, the environment to the measured signals, and the learned policy to the feedback law. Thus, DRL assumes an interactive environment or, equivalently, a control plant. The setup of a numerical simulation plant with DRL is challenging and time-consuming. In this work, a novel Python platform, namely DRLinFluids, is developed for this purpose, with DRL for flow control and optimization problems in fluid mechanics. The simulations employ OpenFOAM as a popular, flexible Navier–Stokes solver in industry and academia, and Tensorforce or Tianshou as widely used versatile DRL packages. The reliability and efficiency of DRLinFluids are demonstrated for two wake stabilization benchmark problems. DRLinFluids significantly reduces the application effort of DRL in fluid mechanics, and it is expected to greatly accelerate academic and industrial applications.

At low Reynolds numbers, the wind flow in the wake of a single wind turbine is generally not turbulent. However, turbines in wind farms affect each other's wakes so that a turbulent flow can arise. In the present work, an analogue of this effect for the massless charge carrier flow around obstacles in graphene is outlined. We use a relativistic hydrodynamic simulation to analyze the flow in a sample containing impurities. Depending on the density of impurities in the sample, we indeed find evidence for potentially turbulent flow and discuss experimental consequences., 7 pages, 9 figures

This paper introduces a novel neural network - flow completion network (FCN) - to infer the fluid dynamics, includ-ing the flow field and the force acting on the body, from the incomplete data based on Graph Convolution AttentionNetwork. The FCN is composed of several graph convolution layers and spatial attention layers. It is designed to inferthe velocity field and the vortex force contribution of the flow field when combined with the vortex force map (VFM)method. Compared with other neural networks adopted in fluid dynamics, the FCN is capable of dealing with bothstructured data and unstructured data. The performance of the proposed FCN is assessed by the computational fluiddynamics (CFD) data on the flow field around a circular cylinder. The force coefficients predicted by our model arevalidated against those obtained directly from CFD. Moreover, it is shown that our model effectively utilizes the exist-ing flow field information and the gradient information simultaneously, giving a better performance than the traditionalconvolution neural network (CNN)-based and deep neural network (DNN)-based models. Specifically, among all thecases of different Reynolds numbers and different proportions of the training dataset, the results show that the proposedFCN achieves a maximum norm mean square error of 5.86% in the test dataset, which is much lower than those of thetraditional CNN-based and DNN-based models (42.32% and 15.63% respectively)., 12 pages, 10 figures

We propose a novel trajectory-optimized cluster-based network model (tCNM) for nonlinear model order reduction from time-resolved data following Li et al. [“Cluster-based network model,” J. Fluid Mech. 906, A21 (2021)] and improving the accuracy for a given number of centroids. The starting point is k-means++ clustering, which minimizes the representation error of the snapshots by their closest centroids. The dynamics is presented by “flights” between the centroids. The proposed trajectory-optimized clustering aims to reduce the kinematic representation error further by shifting the centroids closer to the snapshot trajectory and refining state propagation with trajectory support points. Thus, curved trajectories are better resolved. The resulting tCNM is demonstrated for the sphere wake for three flow regimes, including the periodic, quasi-periodic, and chaotic dynamics. The representation error of tCNM is five times smaller as compared to the approximation by the closest centroid. Thus, the error is at the same level as proper orthogonal decomposition (POD) of same order. Yet, tCNM has distinct advantages over POD modeling: it is human interpretable by representing dynamics by a handful of coherent structures and their transitions; it shows robust dynamics by design, i.e., stable long-time behavior; and its development is fully automatable, i.e., it does not require tunable auxiliary closure and other models.

In this study, we perform a numerical analysis of the instability of a ligament in shear flow and investigate the effects of air-liquid shear on the growth rate of the ligament interface, breakup time, and droplet diameter formed by the breakup. The ligament is stretched in the flow direction by the shearing of airflow. Furthermore, as the influence of the shear flow increases, the ligament becomes deformed into a liquid sheet, and a perforation forms at the center of the liquid sheet. The liquid sheet breaks up due to the growth of the perforation and contracts under the influence of surface tension, forming two ligaments with diameters smaller than that of the original ligament. The shearing of the airflow causes the original ligament to elongate, and the cross-section of the ligament becomes elliptical, which increases instability. As a result, the growth rate of the ligament exceeds the theoretical value, and increases with increasing wavenumber of the initial disturbance. Therefore, the diameter of the formed droplets in shear flow decreases due to the increase in the wavenumber that governs the breakup of the ligament, and because the growth rate increases, the breakup time for the ligament decreases. As the velocity difference of the shear flow increases, constrictions of the ligament form earlier and the diameter of the satellite droplet increases. As the diameter of the satellite droplet increases and that of the main droplet decreases, the dispersion of the droplet diameter decreases, making the diameter uniform., 22 pages, 15 figures, 1 table

The oral route is the most common choice for drug administration because of convenience, low cost, and high patient compliance, but is also a complex route. The rate of dissolution and gastric emptying of the dissolved active pharmaceutical ingredient (API) into the duodenum is modulated by factors such as gastric motility, but current in-vitro procedures for assessing drug dissolution are limited in their ability to recapitulate this process. This is particularly relevant for disease conditions, such as gastroparesis, that alter the anatomy and/or physiology of the stomach. In this study we employ a biomimetic in-silico simulator based on the realistic anatomy and morphology of the stomach, to investigate the effect of body posture and stomach motility on drug bioavailability. The simulations show that changes in posture can have a significant (up to 83%) effect on the emptying rate of the API into the duodenum. Similarly, reduction in antral contractility associated with gastroparesis can also significantly reduce the dissolution of the pill as well as emptying of the API into the duodenum. The simulations show that for an equivalent motility index, reduction in gastric emptying due to neuropathic gastroparesis is larger by a factor of about five compared to myopathic gastroparesis., Comment: 32 pages, 8 figures, supplemental material

We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the nonlinear Schr\"odinger equation and investigate the conditions when a quasi-sinusoidal wave becomes unstable with respect to amplitude modulation. The domains of instability are presented in the planes of governing physical parameters; the shapes of the domains exhibit fairly complicated patterns. It is shown that under certain conditions the modulational instability can develop from shorter groups and for fewer wave periods than in the situation of deep-water gravity waves on a free water surface. The modulational instability can occur at the conditions shallower than that known for the free water surface kh = 1.363, where k is the wavenumber and h is the water depth. Estimates of parameters of modulated waves are given for the typical physical conditions of an ice-covered sea., Comment: 31 pages, 10 figures

We consider the stability of two-dimensional viscous flows in an annulus with permeable boundary. In the basic flow, the velocity has nonzero azimuthal and radial components, and the direction of the radial flow can be from the inner cylinder to the outer one or vice versa. In most earlier studies, all components of the velocity were assumed to be given on the entire boundary of the flow domain. Our aim is to study the effect of different boundary conditions on the stability of such flows. We focus on the following boundary conditions: at the inflow part if the boundary (which may be either inner or outer cylinder) all components of the velocity are known; at the outflow part of the boundary (the other cylinder), the normal stress and either the tangential velocity or the tangential stress are prescribed. Both types of boundary conditions are relevant to certain real flows: the first one - to porous cylinders, the second - to flows, where the fluid leaves the flow domain to an ambient fluid which is at rest. It turns out that both sets of boundary conditions make the corresponding steady flows more unstable (compared with earlier works where all components of the velocity are prescribed on the entire boundary). In particular, it is demonstrated that even the classical (purely azimuthal) Couette-Taylor flow becomes unstable to two-dimensional perturbations if one of the cylinders is porous and the normal stress (rather than normal velocity) is prescribed on that cylinder.

Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by $\beta$-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. To extract these LVs, their independence and information intensity are quantitatively scrutinized in a two-dimensional transonic flow benchmark problem. Then, the physical meanings of the physics-aware LVs are thoroughly investigated and we confirmed that with appropriate hyperparameter $\beta$, they actually correspond to the generating factors of the training dataset, Mach number and angle of attack. To the best of the authors' knowledge, our work is the first to practically confirm that $\beta$-variational autoencoder can automatically extract the physical generating factors in the field of applied physics. Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared with conventional ROMs, and its validity and efficiency are successfully verified.

In a recent numerical study, we have shown that the unsteady motion past a sphere translating steadily in a wormlike micellar solution is caused due to the breakage of long micelles downstream of the sphere once the Weissenberg number exceeds a critical value based on the two-species Vasquez-Cook-McKinley (VCM) constitutive model for wormlike micelles (C. Sasmal, Unsteady motion past a sphere translating steadily in wormlike micellar solutions: a numerical analysis, Journal of Fluid Mechanics, 912, A52, 2021). This study further shows that this unsteady motion is strongly influenced by the micelle breakage rate and wall slip present on the sphere surface. In particular, we find that the onset of this unsteady motion is delayed to higher values of the Weissenberg number as the micelle breakage rate decreases or, in other words, as the micelles become hard to break. Additionally, we observe that at some values of the micelle breakage rate, a transition in the flow field from steady to unsteady occurs as the Weissenberg number increases, and then again, a transition from unsteady to steady occurs as the Weissenberg number further increases. Therefore, there is a window of the Weissenberg number present in which one can see this unsteady motion past the translating sphere. On the other hand, we show that the presence of wall slip on the sphere surface suppresses this unsteady motion past the translating sphere, and a probable explanation for the same is provided in this study.

We investigate how ferrofluid droplets suspended in a wall-bounded shear flow can organize when subjected to an external magnetic field. By tuning the magnitude of the external magnetic field, we find that the ferrofluid droplets form chain-like structures in the flow direction when the magnetic field is weak, while forming a crystal-like pattern in a strong magnetic field. We provide the phase diagram and the critical conditions for this chain-to-crystal transition, by applying both numerical simulations and analytic calculations. We also examine how the organized patterns of the ferrofluid droplets can be controlled by simply changing the direction of the magnetic field. This work demonstrates new aspects of field-controllable ferrofluid droplets as a configurable and reprocessable metamaterial.