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The numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A comparatively new approach in this context is to combine the good approximation properties of neural networks (for parameter dependence) with the classical finite element method (for discretization). However, instead of considering the solution mapping of the PDE from the parameter space into the FEM-discretized solution space as a purely data-driven regression problem, so-called physically informed regression problems have proven to be useful. In these, the equation residual is minimized during the training of the neural network, i.e. the neural network "learns" the physics underlying the problem. In this paper, we extend this approach to saddle-point and non-linear fluid dynamics problems, respectively, namely stationary Stokes and stationary Navier-Stokes equations. In particular, we propose a modification of the existing approach: Instead of minimizing the plain vanilla equation residual during training, we minimize the equation residual modified by a preconditioner. By analogy with the linear case, this also improves the condition in the present non-linear case. Our numerical examples demonstrate that this approach significantly reduces the training effort and greatly increases accuracy and generalizability. Finally, we show the application of the resulting parameterized model to a related inverse problem.

The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS formulations for the corresponding elastance and mobility problems. The elastance problem computes the potentials of conductors with given net charges, while the mobility problem -- crucial to rheology and complex fluid applications -- computes rigid body velocities given net forces and torques on the particles. The key idea is orthogonal projection of the net charge (or forces and torques) in a rectangular variant of a "completion flow". The proposal is compatible with one-body preconditioning, resulting in well-conditioned square linear systems amenable to fast multipole accelerated iterative solution, thus a cost linear in the particle number. For large suspensions with moderate lubrication forces, MFS sources on inner proxy-surfaces give accuracy on par with a well-resolved boundary integral formulation. Our several numerical tests include a suspension of 10000 nearby ellipsoids, using 26 million total preconditioned degrees of freedom, where GMRES converges to five digits of accuracy in under two hours on one workstation., Comment: 26 pages, 10 figures

Dolphin swimming has been a captivating area of study, yet the hydrodynamics of the dorsal fin remain underexplored. In this study, we present three-dimensional simulations of flow around a wall-mounted dolphin dorsal fin, derived from a real dolphin scan. The NEK5000 (spectral element method) is employed with a second-order hex20 mesh to ensure high accuracy and computational efficiency in the simulations. A total of 13 cases were simulated, covering angles of attack (AoA) ranging from $0^\circ$ to $60^\circ$ and Reynolds numbers ($\text{Re}$) between 691 and 2000. Our results show that both drag and lift increase significantly with the AoA. Almost no vortex is observed at $\text{AoA} = 0^\circ$, whereas complex vortex structures emerge for $\text{AoA} \geq 30^\circ$, including half-horseshoe, hairpin, arch, and wake vortices. This study offers insights that could inform the design of next-generation underwater robots, heat exchangers, and submarine sails., Comment: 18 pages

Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use the variational form of the PDE residuals in their loss function. Although hp-VPINNs have shown promise over traditional PINNs, they suffer from higher training times and lack a framework capable of handling complex geometries, which limits their application to more complex PDEs. As such, hp-VPINNs have not been applied in solving the Navier-Stokes equations, amongst other problems in CFD, thus far. FastVPINNs was introduced to address these challenges by incorporating tensor-based loss computations, significantly improving the training efficiency. Moreover, by using the bilinear transformation, the FastVPINNs framework was able to solve PDEs on complex geometries. In the present work, we extend the FastVPINNs framework to vector-valued problems, with a particular focus on solving the incompressible Navier-Stokes equations for two-dimensional forward and inverse problems, including problems such as the lid-driven cavity flow, the Kovasznay flow, and flow past a backward-facing step for Reynolds numbers up to 200. Our results demonstrate a 2x improvement in training time while maintaining the same order of accuracy compared to PINNs algorithms documented in the literature. We further showcase the framework's efficiency in solving inverse problems for the incompressible Navier-Stokes equations by accurately identifying the Reynolds number of the underlying flow. Additionally, the framework's ability to handle complex geometries highlights its potential for broader applications in computational fluid dynamics. This implementation opens new avenues for research on hp-VPINNs, potentially extending their applicability to more complex problems., Comment: 18 pages, 13 tables and 20 figures

This letter presents new nontrivial stochastic identities for random isotropic second rank tensor fields. They can be considered as criteria of statistical isotropy in turbulent flows of any nature. The case of axial symmetry is also considered. We confirm the validity of the identities using different direct numerical simulations of turbulent flows., Comment: 7 pages, 4 figures

The accurate quantification of wall-shear stress dynamics is of substantial importance for various applications in fundamental and applied research, spanning areas from human health to aircraft design and optimization. Despite significant progress in experimental measurement techniques and post-processing algorithms, temporally resolved wall-shear stress dynamics with adequate spatial resolution and within a suitable spatial domain remain an elusive goal. To address this gap, we introduce a deep learning architecture that ingests wall-parallel velocity fields from the logarithmic layer of turbulent wall-bounded flows and outputs the corresponding 2D wall-shear stress fields with identical spatial resolution and domain size. From a physical perspective, our framework acts as a surrogate model encapsulating the various mechanisms through which highly energetic outer-layer flow structures influence the governing wall-shear stress dynamics. The network is trained in a supervised fashion on a unified dataset comprising direct numerical simulations of statistically 1D turbulent channel and spatially developing turbulent boundary layer flows at friction Reynolds numbers ranging from 390 to 1,500. We demonstrate a zero-shot applicability to experimental velocity fields obtained from Particle-Image Velocimetry measurements and verify the physical accuracy of the wall-shear stress estimates with synchronized wall-shear stress measurements using the Micro-Pillar Shear-Stress Sensor for Reynolds numbers up to 2,000. In summary, the presented framework lays the groundwork for extracting inaccessible experimental wall-shear stress information from readily available velocity measurements and thus, facilitates advancements in a variety of experimental applications.

Active grids operated with random protocols are a standard way to generate large Reynolds number turbulence in wind and water tunnels. But anomalies in the decay and third-order scaling of active-grid turbulence have been reported. We combine Laser Doppler Velocimetry and hot-wire anemometry measurements in a wind tunnel, with machine learning techniques and numerical simulations, to gain further understanding on the reasons behind these anomalies. Numerical simulations that incorporate the statistical anomalies observed in the experimental velocity field near the active grid can reproduce the experimental anomalies observed later in the decay. The results indicate that anomalies in experiments near the active grid introduce correlations in the flow that persist for long times, and result in the flow being statistically different from homogeneous and isotropic turbulence.

A methodology is built to model and simulate the dynamics of domain coarsening of a two-phase ternary liquid with an arbitrary phase diagram. High numerical performance is obtained through the use of the phase field-method for interface capturing, a lattice Boltzmann method numerical scheme for all the model equations, and a portable, parallel simulation code running on multiple GPUs. The model is benchmarked against an analytic solution for a ternary diffusion couple. It also reproduces the well-known power law for droplet coarsening during Ostwald ripening without fluid flow. Large-scale simulations with flow illustrate the effects of momentum transport and buoyancy, as well as droplet coalescence and sedimentation., Comment: 40 pages, 8 figures

Data-driven RANS modeling is emerging as a promising methodology to exploit the information provided by high-fidelity data. However, its widespread application is limited by challenges in generalization and robustness to inconsistencies between input data of varying fidelity levels. This is especially true for thermal turbulent closures, which inherently depend on momentum statistics provided by low or high fidelity turbulence momentum models. This work investigates the impact of momentum modeling inconsistencies on a data-driven thermal closure trained with a dataset with multiple fidelity (DNS and RANS). The analysis of the model inputs shows that the two fidelity levels correspond to separate regions in the input space. It is here shown that such separation can be exploited by a training with heterogeneous data, allowing the model to detect the level of fidelity in its inputs and adjust its prediction accordingly. In particular, a sensitivity analysis and verification shows that such a model can leverage the data inconsistencies to increase its robustness. Finally, the verification with a CFD simulation shows the potential of this multi-fidelity training approach for flows in which momentum statistics provided by traditional models are affected by model uncertainties.

Fluid injections can induce aseismic slip, resulting in stress changes that may propagate faster than pore pressure diffusion, potentially triggering seismicity at significant distances from injection wells. Constraining the maximum extent of these aseismic ruptures is thus important for better delineating the influence zone of injections concerning their seismic hazard. Here we derive a scaling relation based on rupture physics for the maximum size of aseismic ruptures, accounting for fluid injections with arbitrary flow rate histories. Moreover, based on mounting evidence that the moment release during these operations is often predominantly aseismic, we derive a scaling relation for the maximum magnitude of aseismic slip events. Our theoretical predictions are consistent with observations over a broad spectrum of event sizes, from laboratory to real-world cases, indicating that fault-zone storativity, background stress state, and injected fluid volume are key determinants of the maximum size and magnitude of injection-induced slow slip events., Comment: 29 pages, 6 figures

We study the coupled vibrational dynamics of sub-MHz self-oscillating bubbles at separations of 14 to 92 {\mu}m. Two vapor-rich microbubbles are generated via photothermal heating; their interactions are captured in real space and time via a high-speed camera. By controlling the distance between bubbles with micrometer precision, we induce in- and anti-phase hybridized vibrations, with mode frequencies varying from 0.5 to 0.8 MHz. The observed coupled modes are reproduced by the extended Rayleigh-Plesset equation that takes pressure interactions between the bubbles into account. Our findings facilitate the optimization of bubble array positioning for spatio-temporal microfluidic control., Comment: 15 pages, 3 figures

The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it restricts the mesh size since the solution of the linear system becomes computationally intractable when the mesh resolution increases. The reliance on the ability of High-Performance Computers (HPC) to scale up and meet these requirements is myopic; such very high-fidelity simulations require a paradigm shift in computing. This paper presents an exploration of quantum methodologies aimed at achieving high accuracy in solving such a large system of equations. Leveraging recent works in Quantum Linear Solver Algorithms (QLSA) and variational algorithms suitable for Quantum Simulation in HPC, we aspire to push the boundaries of CFD-relevant problems that can be solved on hybrid quantum-classical framework. To this end, we consider the 2D, transient, incompressible, viscous, non-linear coupled Burgers equation as a test problem and investigate the accuracy of our approach by comparing results with a classical linear system of equation solvers, such as the Generalized Minimal RESidual method (GMRES). Through rigorous testing, our findings demonstrate that our quantum methods yield results comparable in accuracy to traditional approaches. Additionally, we demonstrate the accuracy, scalability, and consistency of our quantum method. Lastly, we present an insightful estimation of the resources our quantum algorithm needs to solve systems with nearly 2 billion mesh points.

In this study, we conduct parameter estimation analysis on a data assimilation algorithm for two turbulence models: the simplified Bardina model and the Navier-Stokes-{\alpha} model. Our approach involves creating an approximate solution for the turbulence models by employing an interpolant operator based on the observational data of the systems. The estimation depends on the parameter alpha in the models. Additionally, numerical simulations are presented to validate our theoretical results, Comment: 24 pictures

In the present study, by adopting the advantage of ultrasonic techniques, we developed a Multichannel Pulsed Ultrasonic Doppler Velocimetry (MPUDV) to measure the 2D2C velocity fields of liquid metal flow. Due to the specially designed Ultrasonic host and post-processing scheme, the MPUDV system can reach a high spatiotemporal resolution of 50 Hz and 3 mm. The flow loop contains a cavity test section to ensure a classical recirculating flow was built to validate the accuracy of MPUDV in velocity field measurement. In the initial phase of the study, water with tracer particles was selected as the working liquid to ensure the velocity field measurements by the well-developed Particle Image Velocimetry (PIV). A comparison of the data obtained from the PIV and MPUDV methods revealed less than 3 differences in the 2D2C velocity field between the two techniques during simultaneous measurements of the same flow field. This finding strongly demonstrates the reliability of the MPUDV method developed in this paper. Moreover, the ternary alloy GaInSn was selected as the working liquid in the flow loop to validate the efficacy of the MPUDV in measuring 2D-2C velocity fields. A series of tests were conducted in the cavity at varying Reynolds numbers, ranging from 9103 to 24123. The measurements demonstrated that the MPUDV could accurately measure the flow structures characterized by a central primary circulation eddy and two secondary eddies in the opaque liquid metal. Furthermore, it was found that the vortex center of the primary circulating eddy and the size of the secondary eddies undergo significant alterations with varying Reynolds numbers, indicating the influence of inertial force on the flow characteristics in the recirculating flow. It is therefore demonstrated that the current MPUDV methodology is applicable for measuring a 2D2C velocity field in opaque liquid metal flows., Comment: 23 pages, 12 figures

This paper presents a new model for the generation of axisymmetric concentrated vortices. The solution of a nonlinear equation for internal gravity waves in an unstable stratified atmosphere is obtained and analyzed within the framework of ideal hydrodynamics. The corresponding expressions describing the dependences on the radius for the radial and vertical velocity components in the inner and outer regions of the vortex include combinations of Bessel functions and modified Bessel functions. The proposed new nonlinear analytical model makes it possible to study the structure and nonlinear dynamics of vortices in the radial and vertical regions. The vortex is limited in height. The maximum vertical velocity component is reached at a certain height. Below this height, radial flows converge towards the axis, and above it, an outflow occurs. The resulting instability in the stratified atmosphere leads to an increase in the radial and vertical velocity components according to the hyperbolic sine law, which turns into exponential growth. The characteristic growth time is determined by the inverse growth rate of the instability. The formation of vortices with finite velocity components, which increase with time, is analyzed. The radial structure of the azimuthal velocity is determined by the structure of the initial perturbation and can change with height. The maximum rotation is reached at a certain height. The growth of the azimuth velocity occurs according to a super-exponential law., Comment: 17 pages, 4 figures. arXiv admin note: text overlap with arXiv:2408.14210

We present experimental evidence of a thermoelectric effect at the interface between two liquid metals. Using superimposed layers of mercury and gallium in a cylindrical vessel operating at room temperature, we provide a direct measurement of the electric current generated by the presence of a thermal gradient along a liquid-liquid interface. At the interface between two liquids, temperature gradients induced by thermal convection lead to a complex geometry of electric currents, ultimately generating current densities near boundaries that are significantly higher than those observed in conventional solid-state thermoelectricity. When a magnetic field is applied to the experiment, an azimuthal shear flow, exhibiting opposite circulation in each layer, is generated. Depending on the value of the magnetic field, two different flow regimes are identified, in good agreement with a model based on the spatial distribution of thermoelectric currents, which has no equivalent in solid systems. Finally, we discuss various applications of this new effect, such as the efficiency of liquid metal batteries., Comment: 14 pages, 13 figures

We investigate the fluid-solid interaction of suspensions of Kolmogorov-size spherical particles moving in homogeneous isotropic turbulence at a microscale Reynolds number of $Re_\lambda \approx 140$. Two volume fractions are considered, $10^{-5}$ and $10^{-3}$, and the solid-to-fluid density ratio is set to $5$ and $100$. We present a comparison between interface-resolved (PR-DNS) and one-way-coupled point-particle (PP-DNS) direct numerical simulations. We find that the modulated energy spectrum shows the classical $-5/3$ Kolmogorov scaling in the inertial range of scales and a $-4$ scaling at smaller scales, with the latter resulting from a balance between the energy injected by the particles and the viscous dissipation, in an otherwise smooth flow. An analysis of the small-scale flow topology shows that the particles mainly favour events with axial strain and vortex compression. The dynamics of the particles and their collective motion studied for PR-DNS are used to assess the validity of the PP-DNS. We find that the PP-DNS predicts fairly well both the Lagrangian and Eulerian statistics of the particles motion for the low-density case, while some discrepancies are observed for the high-density case. Also, the PP-DNS is found to underpredict the level of clustering of the suspension compared to the PR-DNS, with a larger difference for the high-density case.

In this paper, we construct a pretraining framework for fluid environment perception, which includes an information compression model and the corresponding pretraining method. We test this framework in a two-cylinder problem through numerical simulation. The results show that after unsupervised pretraining with this framework, the intelligent agent can acquire key features of surrounding fluid environment, thereby adapting more quickly and effectively to subsequent multi-scenario tasks. In our research, these tasks include perceiving the position of the upstream obstacle and actively avoiding shedding vortices in the flow field to achieve drag reduction. Better performance of the pretrained agent is discussed in the sensitivity analysis.

Providing a compelling derivation of Kolmogorov turbulence is a fascinating open challenge in field theory. Here, we pose a more modest question: if we had a field-theoretic description of Kolmogorov turbulence, could we use it to describe deviations caused, for example, by adding a polymer additive or by relativistic corrections? To investigate this issue, we assume a description of developed, homogeneous, and isotropic turbulence along the lines of Martin, Siggia, and Rose, and we work out the first corrections to the equal-time, two-point spectrum caused by adding non-Newtonian terms to the fluid stress tensor. While the results are not conclusive, they show a promising resemblance to turbulent spectra found in both experiments and large-scale numerical simulations., Comment: 16 pages, 1 figure

Recent studies focusing on the response of turbulent boundary layers (TBL) to a step-change in roughness have provided insight into the scaling and characterisation of TBLs and the development of the internal layer. Although various step-change combinations have been investigated, ranging from smooth-to-rough to rough-to-smooth, the "minimum" required roughness fetch length over which the TBL returns to its homogeneously rough behaviour remains unclear. Moreover, the relationship between a finite- and infinite-fetch roughness function (and the equivalent sandgrain roughness) is also unknown. In this study, we determine the minimum "equilibrium fetch length" for TBL developing over a smooth-to-rough step-change as well as the expected error in local skin friction if the fetch length is under this minimum threshold. An experimental study is carried out where the flow is initially developed over a smooth wall, and then a step-change is introduced using patches of P24 sandpaper. 12 roughness fetch lengths are tested in this study, systematically increasing from $L = 1\delta_2$ up to $L = 39\delta_2$ (where \textit{L} is the roughness fetch length and $\delta_2$ is the TBL thickness of the longest fetch case), measured over a range of Reynolds numbers ($4\cdot10^2 \leq Re_\tau \leq 2\cdot10^5$). Results show that the minimum fetch length needed to achieve full equilibrium recovery is around $20\delta_2$. Furthermore, we observe that $C_f$ recovers to within 10\% of its recovered value for fetch lengths $\geq 5\delta_2$. This information allows us to incorporate the effects of roughness fetch length on the skin friction and roughness function.

This paper develops a novel multi-relaxation-time (MRT) lattice Boltzmann method (LBM) for solving the volume averaged Navier-Stokes equations (VANSE). Different from the approach given in [1], this method is rooted in the widely-adopted density equilibrium distribution, which provides possibility for simulating scenarios where fluid compressibility cannot be ignored, e.g., thermal and multiphase flows. The Chapman-Enskog analysis is presented to confirm the consistency of this scheme at macroscopic level. Some numerical experiments further demonstrate that it achieves second-order convergence and exhibits better numerical performance over previous schemes as reported [2-4]., Comment: 9 pages

A droplet placed on a hydrophilic conical fiber tends to move toward the end of larger radii due to capillary action. Experimental investigations are performed to explore the dynamics of droplets with varying viscosities and volumes on different fibers at the microscale. Droplets are found to accelerate initially and subsequently decelerate during migration. A dynamic model is developed to capture dynamics of the droplet migration, addressing the limitations of previous equilibrium-based scaling laws. Both experimental results and theoretical predictions indicate that droplets on more divergent fibers experience a longer acceleration phase. Additionally, gravitational effects are pronounced on fibers with small cone angles, exerting a substantial influence on droplet migration even below the capillary scale. Moreover, droplets move more slowly on dry fibers compared to those prewetted with the same liquid, primarily attributed to the increased friction. The experiments reveal the formation of a residual liquid film after droplet migration on dry fibers, leading to considerable volume loss in the droplets. To encompass the intricacies of migration on dry fibers, the model is refined to incorporate a higher friction coefficient and variable droplet volumes, providing a more comprehensive depiction of the underlying physics.

We describe the implementation of a 3d Lagrangian particle tracking (LPT) system based on event-based vision (EBV) and demonstrate its application for the near-wall characterization of a turbulent boundary layer (TBL) in air. The viscous sublayer of the TBL is illuminated by a thin light sheet that grazes the surface of a thin glass window inserted into the wind tunnel wall. The data simultaneously captured by three synchronized event-cameras is used to reconstruct the 3d particle tracks within 400 $\mu$m of the wall on a field of view of 12.0 mm x 7.5 mm. The velocity and position of particles within the viscous sublayer permit the estimation of the local vector of the unsteady wall shear stress (WSS) under the assumption of linearity between particle velocity and WSS. Thereby, time-evolving maps of the unsteady WSS and higher order statistics are obtained that are in agreement with DNS data at matching Reynolds number. Near-wall particle acceleration provide the rate of change of the WSS which exhibits fully symmetric log-normal superstatistics. Two-point correlations of the randomly spaced WSS data are obtained by a bin-averaging approach and reveal information on the spacing of near-wall streaks. The employed compact EBV hardware coupled with suited LPT tracking algorithms provide data quality on par with currently used, considerably more expensive, high-speed framing cameras., Comment: 30 pages, 18 figures, 3 tables, submitted to Experiments in Fluids

Solute gradients next to an interface drive a diffusioosmotic flow, the origin of which lies in the intermolecular interactions between the solute and the interface. These flows on the surface of colloids introduce an effective slip velocity, driving their diffusiophoretic migration. In confined environments, we expect the interplay between diffusiophoretic migration and diffusioosmotic flows near the walls to govern the motion of colloids. These near-wall osmotic flows are, however, often considered weak and neglected. Here, using microfluidic experiments in a T-junction, numerical simulations, and theoretical modeling, we show that the interplay between osmotic and phoretic effects leads to unexpected outcomes: forming a colloidal vortex in the absence of inertial effects, and demixing and focusing of the colloids in the direction opposite to what is commonly expected from diffusiophoresis alone. We show these colloidal vortices to be persistent for a range of salt types, salt gradients, and flow rates, and establish a criterion for their emergence. Our work sheds light on how boundaries modulate the solute-mediated transport of colloids in confined environments.

The vertical transport of solid material in a stratified medium is fundamental to a number of environmental applications, with implications for the carbon cycle and nutrient transport in marine ecosystems. In this work, we study the diffusion-limited settling of highly porous particles in a density-stratified fluid through a combination of experiment, analysis, and numerical simulation. By delineating and appealing to the diffusion-limited regime wherein buoyancy effects due to mass adaptation dominate hydrodynamic drag, we derive a simple expression for the steady settling velocity of a sphere as a function of the density, size, and diffusivity of the solid, as well as the density gradient of the background fluid. In this regime, smaller particles settle faster, in contrast with most conventional hydrodynamic drag mechanisms. Furthermore, we outline a general mathematical framework for computing the steady settling speed of a body of arbitrary shape in this regime and compute exact results for the case of general ellipsoids. Using hydrogels as a highly porous model system, we validate the predictions with laboratory experiments in linear stratification for a wide range of parameters. Lastly, we show how the predictions can be applied to arbitrary slowly varying background density profiles and demonstrate how a measured particle position over time can be used to reconstruct the background density profile.

We present numerical analysis of the lateral movement of spherical capsule in the steady and pulsatile channel flow of a Newtonian fluid, for a wide range of oscillatory frequency. Each capsule membrane satisfying strain-hardening characteristic is simulated for different Reynolds numbers Re and capillary numbers Ca. Our numerical results showed that capsules with high Ca exhibit axial focusing at finite Re similarly to the inertialess case. We observe that the speed of the axial focusing can be substantially accelerated by making the driving pressure gradient oscillating in time. We also confirm the existence of an optimal frequency which maximizes the speed of axial focusing, that remains the same found in the absence of inertia. For relatively low Ca, on the other hand, the capsule exhibits off-centre focusing, resulting in various equilibrium radial positions depending on Re. Our numerical results further clarifies the existence of a specific Re for which the effect of the flow pulsation to the equilibrium radial position is maximum. The roles of channel size and viscosity ratio on the lateral movements of the capsule are also addressed.

Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration, noise and erosion damage. Modelling such a unsteady and highly turbulent flow remains a challenging issue. In this paper, cloud cavitating flow in a venturi is calculated using the Detached Eddy Simulation (DES) model combined with the Merkle model. The Adaptive Mesh Refinement (AMR) method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi. The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle. In addition, the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations. While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat, it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation . Additionally, the AMR calculations is unable to reproduce the cavity width as observed in the experiments. Therefore, while AMR promises to speed the process significantly by refining grid only in regions of interest, it is comparatively in line with a traditional calculation for cavitating flows. Thus, this study intends to provide a reference to employing AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.

This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the central gradient-based reconstruction approach presented in [1] (Hoffmann, Chamarthi and Frankel, JCP 2024). By leveraging a combination of conservative and characteristic variable reconstruction, the proposed approach demonstrates oscillation-free results while effectively reducing computational costs and improving the results. Furthermore, the adaptive central-upwind algorithm is generalized to be compatible not only with the gradient-based reconstruction as in [1] but with other existing methods. In this regard, with the proposed algorithm, the standard fifth/sixth-order reconstruction scheme has also been shown to outperform existing schemes with a 20-30% reduction in computational expense with improved results. Notably, the proposed approach has successfully prevented the generation of spurious vortices in the double shear layer test cases, even with linear schemes, showcasing its robustness and effectiveness., Comment: 25 pages, 12 Figures

Simulations of coronary hemodynamics have improved non-invasive clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree. This ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating branch-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. We assimilate patient-specific measurements of myocardial blood flow from CT myocardial perfusion imaging to estimate branch-specific coronary flows. We use adaptive Markov Chain Monte Carlo sampling to estimate the joint posterior distributions of model parameters with simulated noise in the clinical data. Additionally, we determine the posterior predictive distribution for relevant quantities of interest using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. Our framework recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement uncertainty. We substantially shrink the confidence intervals for estimated quantities of interest compared to single-fidelity and state-of-the-art multi-fidelity Monte Carlo methods. This is especially true for quantities that showed limited correlation between the low- and high-fidelity model predictions. Moreover, the proposed estimators are significantly cheaper to compute for a specified confidence level or variance.

A novel single MRT-featured lattice Boltzmann method (SmrtLBM) is introduced. The intricate algorithm of the multiple-relaxation-time (MRT) collision operator is reimagined and distilled into a streamlined, single-relaxation-time-like scheme. This innovation preserves the simplicity and efficiency of the conventional single-relaxation-time approach while inheriting the enhanced stability characteristic of the MRT techniques, making it a powerful tool for simulating complex fluid flows. Rigorous numerical testing on cavity flows demonstrates that SmrtLBM accurately captures complex flow characteristics, even in challenging high Reynolds number regimes where precision and stability are crucial. Compared to the traditional single-relaxation-time lattice Boltzmann method, this model offers superior stability and accurate solutions for difficult flows. The SmrtLBM marks a breakthrough in complex fluid simulation through a simple method, offering a new level of efficiency and reliability in tackling challenging flow problems., Comment: 9 pages, 8 figures

The development of a wall model using machine learning methods for the large-eddy simulation (LES) of separated flows is still an unsolved problem. Our approach is to leverage the significance of separated flow data, for which existing theories are not applicable, and the existing knowledge of wall-bounded flows (such as the law of the wall) along with embedded learning to address this issue. The proposed so-called features-embedded-learning (FEL) wall model comprises two submodels: one for predicting the wall shear stress and another for calculating the eddy viscosity at the first off-wall grid nodes. We train the former using the wall-resolved LES data of the periodic hill flow and the law of the wall. For the latter, we propose a modified mixing length model, with the model coefficient trained using the ensemble Kalman method. The proposed FEL model is assessed using the separated flows with different flow configurations, grid resolutions, and Reynolds numbers. Overall good a posteriori performance is observed for predicting the statistics of the recirculation bubble, wall stresses, and turbulence characteristics. The statistics of the modelled subgrid-scale (SGS) stresses at the first off-wall grids are compared with those calculated using the wall-resolved LES data. The comparison shows that the amplitude and distribution of the SGS stresses obtained using the proposed model agree better with the reference data when compared with the conventional wall model.

This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the mesh adaptation process for staggered schemes, leveraging a unique cell-tree-vertex data structure that expedites the construction of conservation elements and simplifies the interconnection among computational cells. The integration of second-order a-{\alpha}, Courant number-insensitive, and upwind CESE schemes with this adaptation algorithm is demonstrated. Numerical simulations focusing on compressible inviscid flows are carried out to validate the effectiveness of the extended schemes and the adaptation algorithm.

We investigate the emergent dynamics of a rapidly yawing spheroidal swimmer interacting with a viscous shear flow. We show that the rapid yawing generates non-axisymmetric emergent effects, with the active swimmer behaving as an effective passive particle with two orthogonal planes of symmetry. The shape of the equivalent effective particle is different to the average shape of the active particle. Moreover, despite having two planes of symmetry, the equivalent passive particle is not an ellipsoid in general, except for specific scenarios in which the effective shape is a spheroid. We use a multiple scales analysis for systems to derive the emergent swimmer behaviour, which requires solving a nonautonomous nonlinear 3D dynamical system, and we validate our analysis via comparison to numerical simulations.

We study the effect of shear due to the large scale flow (LSF) on the heat flux in Rayleigh B'enard convection for a range of near-plate Rayleigh numbers $8\times 10^7 \leq Ra_w \leq 5\times 10^{14}$, by studying its effect on the local boundary layers (BLs) on either sides of the plumes, which are much thinner than the global shear BL created by the LSF velocity $V_F$. Considering these local BLs forced externally by the LSF, we obtain a fifth order algebraic equation for the local boundary layer thicknesses. Solving these equations numerically using $Re$ relations for aspect ratios $\Gamma=1$ and 0.5, we obtain the variation of the local BL thicknesses with the longitudinal distance for various $Ra_w$. We find that the average shear acting on the edges of these local BLs ($\overline{u|}_{z=\delta}$) increases as $\overline{u|}_{z=\delta} \sim Ra_w^{1/3}$ for $8\times 10^7\leq Ra_w \leq 10^{12}$ at $\Gamma=1$, and as $\overline{u|}_{z=\delta} \sim Ra_w^{0.38}$ for $1\times 10^{11}\leq Ra_w \leq 5\times 10^{14}$ at $\Gamma=0.5$. We then estimate the average local thermal BL thickness to find the global Nusselt number $Nu$.We find that $Nu\sim Ra_w^m$, where $m\approx 0.327$ for $8\times 10^7 \leq Ra_w \leq 1\times 10^{12}$ at $\Gamma=1$, and $m=0.33$ for $1\times10^{11}\leq Ra_w \leq 5\times10^{14}$ at $\Gamma=0.5$. Inspite of the increasing shear on these BLs with increasing $Ra_w$, we then surprisingly obtain the classical 1/3 scaling of flux since the shear forcing acting on those BLs remains sub-dominant compared to the NCBL velocities ($V_{bl}$) within these BLs, upto $Ra_w\leq 5\times10^{14}$.

Bio-inspired flapping wings have been extensively studied for their remarkable aerodynamic performance. Recently, their noise emission has attracted growing interest, but a careful analysis of scaling laws for their sound generation is missing. This work presents scaling laws for the sound generation of bio-inspired flapping wings during hovering flight based on the potential flow theory and Ffowcs Williams-Hawkings acoustic analogy. Direct numerical simulations considering a range of parameters including the Reynolds number, Mach number and wing kinematics confirms that the proposed scaling laws capture the major physics involved and their predictions agree well with the numerical results. The scaling laws can be used as a powerful tool for engineers in the design of micro-aerial vehicles considering both aerodynamics and acoustics performances simultaneously.

This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves into a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.

We investigate continuous generation of bubbles from a bath of air in viscous liquid in a confined geometry. In our original setup, bubbles are spontaneously generated by virtue of buoyancy and a gate placed in the cell: the gate acts like an inverted funnel trapping air beneath it before continuously generating bubbles at the tip. The dynamics is characterized by the period of the bubble formation and the size of bubbles as a function of the amount of air under the gate. By analyzing the data obtained for various parameters, we successfully identified in a clear manner that the dynamics of the bubble formation is governed by dissipation in thin films whose thickness is determined by Derjaguin's law balanced by a gravitational energy change due to buoyancy, after examining numerous possibilities of dissipation, demonstrating the potential of scaling analysis even in extremely complex cases. Furthermore, we uncover a novel type of pinch-off condition, which convincingly explains the size of the bubble created: in the present case viscosity plays a vital role beyond the conventional mechanism of Tate in which gravity competes with capillarity, revealing a general mechanism of pinching-off at low Reynolds number. Accordingly, the present study significantly and fundamentally advance our knowledge of bubble generation and bubble pinch-off in a clear manner with the results relevant for a wide variety of applications in many fields. In particular, the present study demonstrates a new avenue in microfluidics for understanding physical principles by scaling up the system, without losing the characters of the flow at low Reynolds numbers.

Galerkin reduced order models (ROMs), e.g., based on proper orthogonal decomposition (POD) or reduced basis methods, have achieved significant success in the numerical simulation of fluid flows. The ROM numerical analysis, however, is still being developed. In this paper, we take a step in this direction and present a survey of a priori error bounds, with a particular focus on POD-based ROMs. Specifically, we outline the main components of ROM a priori error bounds, emphasize their practical importance, and discuss significant contributions to a priori error bounds for ROMs for fluids.

A pair of Direct Numerical Simulations is used to investigate curvature and pressure effects. One has a Gaussian test bump and a straight opposite wall, while the other has a straight test wall and a blowing/suction distribution on an opposite porous boundary, adjusted to produce the same pressure distribution. The calculation of the transpiration distribution is made in potential flow, ignoring the boundary layer. This problem of specifying a pressure distribution is known to be ill-posed for short waves. We address this issue by considering a pressure distribution that is very smooth compared with the distance from wall to opposite boundary. It is also ill-posed once separation occurs. The pressure distribution of the viscous flow nevertheless ended up very close to the specified one, upstream of separation, and comparisons are confined to that region. In the entry region the boundary layers have essentially the same thicknesses and are well-developed turbulence-wise, which is essential for a valid comparison. The focus is on the attached flow in the favorable and adverse gradients. The convex curvature is strong enough compared with the boundary-layer thickness to make the strain-rate tensor drop to near zero over the top of the bump. An intense internal layer forms in the favorable gradient, an order of magnitude thinner than the incoming boundary layer. The effect of curvature follows expectations: concave curvature moderately raises the skin friction, although without creating Gortler vortices, and convex curvature reduces it. The pressure gradient still dominates the physics. Common turbulence models unfortunately over-predict the skin friction in both flows near its peak, and under-predict the curvature effect even when curvature corrections are included.

Electrolytically generated gas bubbles can significantly hamper the overall electrolysis efficiency. Therefore it is crucial to understand their dynamics in order to optimise water electrolyzer systems. Here we demonstrate a distinct transport mechanism where coalescence with microbubbles drives electrolyte droplets, resulting from the fragmentation of the Worthington jet, into the gas phase during hydrogen evolution reaction, both in normal and microgravity environments. This indicates that the H$_2$ bubble is not only composed of hydrogen gas and vapor but also includes electrolyte fractions. Reminiscent of bursting bubbles on a liquid-gas interface, this behavior results in a flow inside the bubble, which is further affected by Marangoni convection at the gas-electrolyte interface, highlighting interface mobility. In the case of electrode-attached bubbles, the sprayed droplets form electrolyte puddles at the bubble-electrode contact area, affecting the dynamics near the three-phase contact line and favoring bubble detachment from the electrode. The results of this work unravel important insights into the physicochemical aspects of electrolytic gas bubbles, integral for optimizing gas-evolving electrochemical systems. Besides, our findings are essential for studying the limits of jet formation and rupture relevant to acid mist formation in electrowinning, generation of sea spray aerosols, impact of droplets on liquid surfaces, etc., Comment: manuscript: 25 pages, 6 figures; SI: 12 pages, 5 figures, 1 table

The dynamics of inertial particles in fluid flows have been the focus of extensive research due to their relevance in a wide range of industrial and environmental processes. Earlier studies have examined the dynamics of aerosols and bubbles using the Maxey-Riley equation in some standard systems but their dynamics within the traveling wave flow remain unexplored. In this paper, we study the Lagrangian dynamics of inertial particles in the traveling wave flow which shows mixing, and segregation in phase space as well as the formation of Lagrangian Coherent Structures (LCS). We first obtain the finite-time Lyapunov exponent (FTLEs) for the base fluid flow defined by the traveling wave flow using the Cauchy-Green deformation tensor. Further, we extend our calculations to the inertial particles to get the inertial finite-time Lyapunov exponent (iFTLEs). Our findings reveal that heavier inertial particles tend to be attracted to the ridges of the FTLE fields, while lighter particles are repelled. By understanding how material elements in a flow separate and stretch, one can predict pollutant dispersion, optimize the mixing process, and improve navigation and tracking in fluid environments. This provides insights into the complex and non-intuitive behavior of inertial particles in chaotic fluid flows, and may have implications for pollutant transport in wide-ranging fields such as atmospheric and oceanic sciences., Comment: 12 pages, 13 figures

We study the lubricated contact of sliding soft surfaces that are locally patterned but globally cylindrical, held together under an external normal force. The local patterns represent either naturally occurring surface roughness or engineered surface textures. Three dimensionless parameters govern the system: a speed, and the amplitude and wavelength of the pattern. Using numerical solutions of the Reynolds lubrication equation, we investigate the effects of these dimensionless parameters on key variables such as contact pressure and the coefficient of friction of the lubricated system. For small roughness amplitudes, the coefficient of friction increases with roughness. However, our findings reveal that increasing surface roughness beyond a critical value can decrease the friction coefficient, a result that contradicts conventional intuition and classical studies on the lubrication of rigid surfaces. For very large roughness amplitudes, we show that the coefficient of friction drops even below the corresponding smooth case. We support these observations with a combination of perturbation theory and physical arguments, identifying scaling laws for large and small speeds, and for large and small roughness amplitudes. This study provides a quantitative understanding of friction in the contact of soft, wet objects and lays theoretical foundations for incorporating the friction coefficient into haptic feedback systems in soft robotics and haptic engineering.

We investigate experimentally the receding of a contact line when a Peltier module is pulled out of a water bath at constant speed, while a ice layer is also growing at constant speed on the Peltier module. A steady regime is therefore reached for all the parameters used in this studied, corresponding to a dynamical stationnary meniscus. We show that the height of the meniscus provides most of the properties of the flow. For high pulling rate, it is related to the amount of liquid of the equivalent Landau-Levich (LL) film that would be extracted from the bath, which is eventually freezing as the plate is lifted upward. For smaller velocity, so that no LL film would be formed without freezing, the meniscus height is directly linked to the contact angle of water on ice in these conditions. Solving numerically the meniscus equation taking into account the solidifcation of water, our results suggest that the contact angle of water on ice should be around $6^\circ$.

In the present study, we conduct numerical simulations of compressible flows around spheroid particles, for the purpose of refining empirical formulas for drag force, lift force, and pitching torque acting on them. Through an analysis of approximately a thousand numerical simulation cases spanning a wide range of Mach numbers, Reynolds numbers and particle aspect ratios, we first identify the crucial parameters that are strongly correlated with the forces and torques via Spearman correlation analysis, based on which the empirical formulas for the drag force, lift force and pitching torque coefficients are refined. The novel formulas developed for compressible flows exhibit consistency with their incompressible counterparts at low Mach number limits and, moreover, yield accurate predictions with average relative errors of less than 5%. This underscores their robustness and reliability in predicting aerodynamic loads on spheroidal particles under various flow conditions.

Data from fluid flow measurements are typically sparse, noisy, and heterogeneous, often from mixed pressure and velocity measurements, resulting in incomplete datasets. In this paper, we develop a physics-constrained convolutional neural network, which is a deterministic tool, to reconstruct the full flow field from incomplete data. We explore three loss functions, both from machine learning literature and newly proposed: (i) the softly-constrained loss, which allows the prediction to take any value; (ii) the snapshot-enforced loss, which constrains the prediction at the sensor locations; and (iii) the mean-enforced loss, which constrains the mean of the prediction at the sensor locations. The proposed methods do not require the full flow field during training, making it suitable for reconstruction from incomplete data. We apply the method to reconstruct a laminar wake of a bluff body and a turbulent Kolmogorov flow. First, we assume that measurements are not noisy and reconstruct both the laminar wake and the Kolmogorov flow from sensors located at fewer than 1% of all grid points. The snapshot-enforced loss reduces the reconstruction error of the Kolmogorov flow by approximately 25% compared to the softly-constrained loss. Second, we assume that measurements are noisy and propose the mean-enforced loss to reconstruct the laminar wake and the Kolmogorov flow at three different signal-to-noise ratios. We find that, across the ratios tested, the loss functions with harder constraints are more robust to both the random initialization of the networks and the noise levels in the measurements. At high noise levels, the mean-enforced loss can recover the instantaneous snapshots accurately, making it the suitable choice when reconstructing flows from data corrupted with an unknown amount of noise. The proposed method opens opportunities for physical flow reconstruction from sparse, noisy data.

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and enhance score-based diffusion models in field reconstruction tasks, where the goal is to estimate complete spatial fields from partial observations. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions using a learnable integration of sparse observations and interpolated fields as an inductive bias. With refined sensing representations and an unraveled temporal dimension, our method can handle arbitrary moving sensors and effectively reconstruct fields. Furthermore, we conduct a comprehensive benchmark of our approach against a deterministic interpolation-based method across various static and time-dependent PDEs. Our study attempts to addresses the gap in strong baselines for evaluating performance across varying sampling hyperparameters, noise levels, and conditioning methods. Our results show that diffusion models with cross-attention and the proposed conditional encoding generally outperform other methods under noisy conditions, although the deterministic method excels with noiseless data. Additionally, both the diffusion models and the deterministic method surpass the numerical approach in accuracy and computational cost for the steady problem. We also demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results in covariance-based correction tasks using ensemble sampling.

The amplitude modulation phenomena, defined originally by Mathis et al. (J. Fluid Mech., 628, 311-337; 2009), corresponds to a unique non-linear interaction between Reynolds number ($Re_{\tau}$) dependent large-scale motions and $Re_{\tau}$-invariant inner-scale motions observed in canonical wall-bounded flows. While similar non-linear interactions can be observed in non-canonical wall-bounded flows, linking them to amplitude modulation is questionable due to the fact that each non-canonical effect is associated with distinct variations in the energies of both the large and inner scaled motions. This study investigates non-linear triadic interactions as a function of various non-canonical effects by analyzing published hot-wire datasets acquired in the large Melbourne wind tunnel. It is found that triadic interactions, across the entire turbulence scale hierarchy, become statistically significant with increasing intensity of non-canonical effects such as rough walls, pressure gradients, and spanwise or wall-normal forcing. This stands in contrast to previous observations made in canonical flows, where only the interaction between inner scales and inertia-dominated large scales was considered dynamically significant for increasing $Re_{\tau}$. The implications of these findings are discussed for near-wall flow prediction models in non-canonical flows, which must take into account all coexisting non-linear triadic interactions in wall-bounded flows., Comment: Preprint submitted for review to the Physical Review Fluids, with 12 pages and 3 figures

Data from direct numerical simulations of turbulent flows are commonly used to train neural network-based models as subgrid closures for large-eddy simulations; however, models with low a priori accuracy have been observed to fortuitously provide better a posteriori results than models with high a priori accuracy. This anomaly can be traced to a dataset shift in the learning problem, arising from inconsistent filtering in the training and testing stages. We propose a resolution to this issue that uses explicit filtering of the nonlinear advection term in the large-eddy simulation momentum equations to control aliasing errors. Within the context of explicitly-filtered large-eddy simulations, we develop neural network-based models for which a priori accuracy is a good predictor of a posteriori performance. We evaluate the proposed method in a large-eddy simulation of a turbulent flow in a plane channel at $Re_{\tau} = 180$. Our findings show that an explicitly-filtered large-eddy simulation with a filter-to-grid ratio of 2 sufficiently controls the numerical errors so as to allow for accurate and stable simulations., Comment: 20 pages, 13 figures

The present article is devoted to the study of the dynamics of narrowband wave fields within the non-integrable Schamel equation, which plays an important role in plasma physics, wave dynamics in metamaterials, and electrical circuits. A Monte Carlo approach is used to obtain a large number of random independent realizations of the wave fields, allowing for an investigation of the evolution of the following statistical characteristics: spectra, moments, and distribution functions. The simulations are conducted for different values of the Ursell number (the ratio of nonlinearity to dispersion) to study the impact of nonlinearity and dispersion on the processes under consideration.

We present a linear analysis of a minimal model of moist convection under a variety of atmospheric conditions. The stationary solutions that we analyze include both fully saturated and partially unsaturated atmospheres in both unconditionally and conditionally unstable cases. We find that all of the solutions we consider are linearly unstable via exchange of stability when sufficiently driven. The critical Rayleigh numbers vary by over an order of magnitude between unconditionally unstable and conditionally unstable atmospheres. The unsaturated atmospheres are notable for the presence of linear gravity wave-like oscillations even in unstable conditions. We study their eigenfunction structure and find that the buoyancy and moisture perturbations are anticorrelated in $z$, such that regions of negative buoyancy have positive moisture content. We suggest that these features in unsaturated atmospheres may explain the phenomenon of gravity wave shedding by moist convective plumes., Comment: 24 pages, 16 figures