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This paper evaluates the experimental generation of internal solitary waves (ISWs) in a miscible two-layer system with a free surface using a jet-array wavemaker (JAW). Unlike traditional gate-release experiments, the JAW system generates ISWs by forcing a prescribed vertical distribution of mass flux. Experiments examine three different layer-depth ratios, with ISW amplitudes up to the maximum allowed by the extended Korteweg-de Vries (eKdV) solution. Phase speeds and wave profiles are captured via planar laser-induced fluorescence and the velocity field is measured synchronously using particle imaging velocimetry. Measured properties are directly compared with the eKdV predictions. As expected, small- and intermediate-amplitude waves match well with the corresponding eKdV solutions, with errors in amplitude and phase speed below 10%. For large waves with amplitudes approaching the maximum allowed by the eKdV solution, the phase speed and the velocity profiles resemble the eKdV solution while the wave profiles are distorted following the trough. This can potentially be attributed to Kelvin-Helmholtz instabilities forming at the pycnocline. Larger errors are generally observed when the local Richardson number at the JAW inlet exceeds the threshold for instability., Comment: 25 pages, 11 figures

We consider the relationship between modal representations obtained from data-driven decomposition methods and Lagrangian Coherent Structures (LCSs). Mode sensitivity is used to describe this analysis as an extension of the model sensitivity framework developed by Kasz\'as and Haller (2020). The method, based on the computation of the finite-time-Lyapunov exponent, uses modes from fluid data to compute the amplitude perturbations experienced by fluid particle trajectories along with their sensitivity to initial conditions. Demonstrations of the method are presented with both periodic and turbulent flows, including a kinematic flow model, experimental data from the wake past an oscillating foil, numerical data of the classical cylinder wake flow, and a direct numerical simulation (DNS) of a turbulent channel flow. Mode sensitivity fields reveal both quantitatively and qualitatively how the finite-time Lyapunov exponent fields used to visualize LCSs change due to the influence of modes or external perturbations.

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry (PIV) measurements of the flow field downstream of the foil are presented for a Reynolds number of Re=11$\times$10$^3$ and Strouhal numbers in the range St=0.16-0.35. These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition (opt-DMD) method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum., Comment: 28 pages, 14 figures

Turbulent flows over porous lattices consisting of rectangular cuboid pores are investigated using scale-resolving direct numerical simulations. Beyond a certain threshold which is primarily determined by the wall-normal Darcy permeability, ${K_y}^+$, near-wall turbulence transitions from its canonical regime, marked by the presence of streak-like structures, to another marked by the presence of spanwise coherent structures reminiscent of the Kelvin-Helmholtz (K-H) type of instability. This permeability threshold agrees well with that previously established in studies where permeable-wall boundary conditions had been used as surrogates for a porous substrate. None of the substrates investigated demonstrate any drag reduction relative to smooth-wall turbulent flow. At the permeable surface, a significant component of the flow is that which adheres to the pore geometry and undergoes amplitude modulation (AM). This pore-coherent flow remains notable within the substrates, highlighting the importance of the porous substrate's microstructure when the overlying flow is turbulent, an aspect which cannot be accounted for when using continuum-based approaches to model porous media flows or effective representations such as wall boundary conditions. The severity of the AM is enhanced in the K-H-like regime, which has implications when designing porous substrates for transport processes. This suggests that the surface of the substrate can have a geometry which is different than the rest of it and tailored to influence the overlying flow in a particular way.

Bluff body wakes in stratified fluids are known to exhibit a rich range of dynamic behavior that can be categorized into different regimes based on Reynolds number ($Re$) and Froude number ($Fr$). Topological differences in wake structure across these different regimes have been clarified recently through the use of Dynamic Mode Decomposition (DMD) on Direct Numerical Simulation (DNS) and laboratory data for a sphere in a stratified fluid for $Re\in [200,1000]$ and $Fr\in[0.5,16]$. In this work, we attempt to identify the dynamic regime from limited measurement data in a stratified wake with (nominally) unknown $Re$ and $Fr$. A large database of candidate basis functions is compiled by pooling the DMD modes obtained in prior DNS. A sparse model is built using the Forward Regression with Orthogonal Least Squares (FROLS) algorithm, which sequentially identifies DMD modes that best represent the data and calibrates their amplitude and phase. After calibration, the velocity field can be reconstructed using a weighted combination of the dominant DMD modes. The dynamic regime for the measurements is estimated via a projection-weighted average of $Re$ and $Fr$ corresponding to the identified modes. Regime identification is carried out from a limited number of 2D velocity snapshots from numerical and experimental datasets, as well as 3 point measurements in the wake of the body. A metric to assess confidence is introduced based on the observed predictive capability. This approach holds promise for the implementation of data-driven fluid pattern classifiers., Comment: 27 pages, 17 captioned figures. Manuscript submitted to Physical Review Fluids on 27 Sep 2021. First revision submitted on 4 Feb 2022

Airborne transmission is now believed to be the primary way that COVID-19 spreads. We study the airborne transmission risk associated with holding in-person classes on university campuses. We utilize a model for airborne transmission risk in an enclosed room that considers the air change rate for the room, mask efficiency, initial infection probability of the occupants, and also the activity level of the occupants. We introduce, and use for our evaluations, a metric $R_0^{eff}$ that represents the ratio of new infections that occur over a week due to classroom interactions to the number of infected individuals at the beginning of the week. This can be seen as a surrogate for the well-known $R_0$ reproductive number metric, but limited in scope to classroom interactions and calculated on a weekly basis. The simulations take into account the possibility of repeated in-classroom interactions between students throughout the week. We presented model predictions were generated using Fall 2019 and Fall 2020 course registration data at a large US university, allowing us to evaluate the difference in transmission risk between in-person and hybrid programs. We quantify the impact of parameters such as reduced occupancy levels and mask efficacy. Our simulations indicate that universal mask usage results in an approximately $3.6\times$ reduction in new infections through classroom interactions. Moving 90% of the classes online leads to about $18\times$ reduction in new cases. Reducing class occupancy to 20%, by having hybrid classes, results in an approximately $2.15-2.3\times$ further reduction in new infections., Comment: 6 pages, typos corrected, picture of figure 1(f) corrected, added acknowledgments, added funding support

The spread of infectious epidemics is often accelerated by super-spreader events. Understanding their effect is important, particularly in the context of standard epidemiological models, which require estimates for parameters such as $R_0$. In this letter, we show that the effective value of $R_0$ in super-spreader situations is significantly large, of the order of hundreds, suggesting a delta-function-like behavior during the event. Use of a well-mixed room model supports these findings. They elucidate infection kinetic modeling in enclosed environments, which differ from the standard SIR model, and provide expressions for $R_0$ in terms of physical and operational parameters. The overall impact of super-spreader events can be significant, depending on the state of the epidemic and how the infections generated by the event subsequently spread in the community.

Wall-bounded turbulent flows can be challenging to measure within experiments due to the breadth of spatial and temporal scales inherent in such flows. Instrumentation capable of obtaining time-resolved data (e.g., Hot-Wire Anemometers) tends to be restricted to spatially-localized point measurements; likewise, instrumentation capable of achieving spatially-resolved field measurements (e.g., Particle Image Velocimetry) tends to lack the sampling rates needed to attain time-resolution in many such flows. In this study, we propose to fuse measurements from multi-rate and multi-fidelity sensors with predictions from a physics-based model to reconstruct the spatiotemporal evolution of a wall-bounded turbulent flow. A "fast" filter is formulated to assimilate high-rate point measurements with estimates from a linear model derived from the Navier-Stokes equations. Additionally, a "slow" filter is used to update the reconstruction every time a new field measurement becomes available. By marching through the data both forward and backward in time, we are able to reconstruct the turbulent flow with greater spatiotemporal resolution than either sensing modality alone. We demonstrate the approach using direct numerical simulations of a turbulent channel flow from the Johns Hopkins Turbulence Database. A statistical analysis of the model-based multi-sensor fusion approach is also conducted.

This letter considers control of a radially symmetric tripedal friction-driven robot. The robot features 3 servo motors mounted on a 3-D printed chassis 7 cm from the center of mass and separated 120 degrees. These motors drive limbs, which impart frictional reactive forces on the body. Experimental observations performed on a uniform friction surface validated a mathematical model for robot motion. This model was used to create a gait map, which features instantaneous omni-directional control. We demonstrated line following using live feedback from an overhead tracking camera. Proportional-Integral error compensation performance was compared to a basic position update procedure on a rectangular course. The controller reduced path error by approximately $46\%$. The error compensator is also able to correct for aerodynamic disturbances generated by a high-volume industrial fan with a mean flow speed of $5.5ms^{-1}$, reducing path error by $65\%$ relative to the basic position update procedure., Comment: 6 pages, 6 figures

Recent simulations indicate that streamwise-preferential porous materials have the potential to reduce drag in wall-bounded turbulent flows(Gomez-de-Segura & Garcia-Mayoral 2019). This paper extends the resolvent formulation to study the effect of such anisotropic permeable substrates on turbulent channel flow. Under the resolvent formulation, the Fourier-transformed Navier-Stokes equations are interpreted as a linear forcing-response system. The nonlinear terms are considered the endogenous forcing in the system that gives rise to a velocity and pressure response. A gain-based decomposition of the forcing-response transfer function---the resolvent operator---identifies response modes (resolvent modes) that are known to reproduce important structural and statistical features of wall-bounded turbulent flows. The effect of permeable substrates is introduced in this framework using the Volume-Averaged Navier-Stokes equations and a generalized form of Darcy's law. Substrates with high streamwise permeability and low spanwise permeability are found to suppress the forcing-response gain for the resolvent mode that serves as a surrogate for the energetic near-wall cycle. This reduction in mode gain is shown to be consistent with the drag reduction trends predicted by theory and observed in numerical simulations. Simulation results indicate that drag reduction is limited by the emergence of spanwise rollers resembling Kelvin-Helmholtz vortices beyond a threshold value of wall-normal permeability. The resolvent framework also predicts the conditions in which such energetic spanwise-coherent rollers emerge. These findings suggest that a limited set of resolvent modes can serve as the building blocks for computationally-efficient models that enable the design and optimization of permeable substrates for passive turbulence control., Comment: 24 pages, 8 figures

Recent numerical simulations indicate that streamwise-preferential anisotropic porous materials have the potential to reduce skin friction in turbulent flows through a similar mechanism to riblets. This paper reports particle image velocimetry (PIV) measurements made in turbulent boundary layers at $Re_\tau \approx 360$ over 3D-printed porous substrates exhibiting such streamwise-preferential permeability. The porous material has normalized streamwise permeability $\sqrt{K_{xx}^+}\approx 3.0$ and wall-normal and spanwise permeabilities $\sqrt{K_{yy}^+} = \sqrt{K_{zz}^+} \approx 1.1$. This material is flush-mounted into a cutout in the downstream half of a flat-plate boundary layer setup in a water channel facility. Measurements made at several locations along the porous substrate provide insight into boundary layer development. For fully-developed conditions, the mean profiles show the presence of a logarithmic region over the porous material with similar constants to those found over a smooth wall. A technique that estimates the mean profile at single-pixel resolution from the particle images suggests the presence of an interfacial slip velocity of $U_s^+ \approx \sqrt{K_{xx}^+}$ over the porous substrate. Friction velocity estimates obtained from outer layer fits to the mean profile suggest a marginal increase in drag over the porous substrate. PIV measurements show a decrease in the intensity of streamwise velocity fluctuations in the near-wall region and an increase in the intensity of wall-normal velocity fluctuations. These observations are consistent with simulation results, which suggest that materials with $\sqrt{K_{yy}^+} > 0.4$ are susceptible to the emergence of spanwise rollers similar to Kelvin-Helmholtz vortices that degrade drag reduction performance. Velocity spectra indicate that such structures emerge in the experiments as well.

Laboratory and field measurements made over the past decade have shown the presence of a strong wave-driven mean current in submerged vegetation canopies. Luhar et al. (2010) suggested that this mean current is analogous to the streaming flow generated in wave boundary layers over bare beds, and developed a simple energy and momentum balance model to predict its magnitude. However, this model predicts that the magnitude of the mean current does not depend on canopy spatial density, which is inconsistent with the measurements made by Abdolahpour et al. (2017) in recent laboratory experiments. Motivated by observations that the wave-driven mean flow is most pronounced at the canopy interface, Abdolahpour et al. (2017) proposed an alternate explanation for its origin: that it is driven by the vertical heterogeneity in orbital motion created by canopy drag. Such heterogeneity can give rise to incomplete particle orbits near the canopy interface and a Lagrangian mean current analogous to Stokes drift in the direction of wave propagation. A model guided by this physical insight and dimensional analysis is able to generate much more accurate predictions. This comment aims to reconcile these two different models for the wave-driven mean flow in submerged canopies.

An extended version of the resolvent formulation is used to evaluate the use of anisotropic porous materials as passive flow control devices for turbulent channel flow. The effect of these porous substrates is introduced into the governing equations via a generalized version of Darcy's law. Model predictions show that materials with high streamwise permeability and low wall-normal permeability ($\phi_{xy} = k_{xx}/k_{yy}\gg1$) can suppress resolvent modes resembling the energetic near-wall cycle. Based on these predictions, two anisotropic porous substrates with $\phi_{xy} > 1$ and $\phi_{xy} < 1$ were designed and fabricated for experiments in a benchtop water channel experiment. Particle Image Velocimetry (PIV) measurements were used to compute mean turbulence statistics and to educe coherent structure via snapshot Proper Orthogonal Decomposition (POD). Friction velocity estimates based on the Reynolds shear stress profiles do not show evidence of discernible friction reduction (or increase) over the streamwise-preferential substrate with $\phi_{xy}>1$ relative to a smooth wall flow at identical bulk Reynolds number. A significant increase in friction is observed over the substrate with $\phi_{xy} < 1$. This increase in friction is linked to the emergence of spanwise rollers resembling Kelvin-Helmholtz vortices. Coherent structures extracted via POD analysis show qualitative agreement with model predictions., Comment: 26 pages, 7 figures

Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on Rapid Distortion Theory (RDT) and Taylor's Hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forwards and backwards in time using the PIV snapshots as initial conditions. The flow field in the intervening period is then reconstructed by taking a weighted sum of the forward and backward estimates. This spatiotemporal weighting function is designed to account for the advective nature of the RDT and TH equations. Reconstruction accuracy is evaluated as a function of spatial resolution and reconstruction time horizon using Direct Numerical Simulation data for turbulent channel flow from the Johns Hopkins Turbulence Database. This method reconstructs single-point turbulence statistics well and resolves velocity spectra at frequencies higher than the temporal Nyquist limit of the acquisition system. Reconstructions obtained using a characteristics-based evolution of the flow field under TH prove to be more accurate compared to reconstructions obtained from numerical integration of the discretized forms of RDT and TH. The effect of measurement noise on reconstruction error is also evaluated., Comment: 21 pages, 11 captioned figures

This paper extends the resolvent formalism for wall turbulence proposed by McKeon and Sharma(2010) to account for the effect of streamwise-constant riblets. Under the resolvent formulation, the Navier-Stokes equations are interpreted as a forcing-response system: the nonlinear convective term is interpreted as a feedback forcing on the remaining linear terms, which generates a velocity and pressure response. A gain-based decomposition of the linear forcing-response transfer function --- the resolvent operator --- yields highly amplified velocity and pressure modes, which can be considered key building blocks of the turbulent flow field. Previous work has shown that these high-gain modes provide substantial insight into turbulence statistics, structure, and control of smooth-walled flows. To introduce the effect of riblets within this framework, a linear spatially-varying body force is added to the governing equations. In other words, volume penalization is used to approximate the surface features. Predictions for spanwise-periodic and streamwise-constant riblets show that specific high-gain modes identified from the modified governing equations reproduce observations made in prior direct numerical simulations with limited computation. The deterioration in performance with increasing riblet size is predicted well and so is the emergence of spanwise rollers resembling Kelvin-Helmholtz vortices. This new modeling framework is also used to pursue limited riblet shape optimization., Comment: 21 pages, 8 figures

This paper reports turbulent boundary layer measurements made over open-cell reticulated foams with varying pore size and thickness, but constant porosity ($\epsilon \approx 0.97$). The foams were flush-mounted into a cutout on a flat plate. A Laser Doppler Velocimeter (LDV) was used to measure mean streamwise velocity and turbulence intensity immediately upstream of the porous section, and at multiple measurement stations along the porous substrate. The friction Reynolds number upstream of the porous section was $Re_\tau \approx 1690$. For all but the thickest foam tested, the internal boundary layer was fully developed by $<10 \delta$ downstream from the porous transition, where $\delta$ is the boundary layer thickness. Fully developed mean velocity profiles showed the presence of a substantial slip velocity at the porous interface ($>30\%$ of the free stream velocity) and a mean velocity deficit relative to the canonical smooth-wall profile further from the wall. While the magnitude of the mean velocity deficit increased with average pore size, the slip velocity remained approximately constant. Fits to the mean velocity profile suggest that the logarithmic region is shifted relative to a smooth wall, and that this shift increases with pore size until it becomes comparable to substrate thickness $h$. For all foams, the turbulence intensity was found to be elevated further into the boundary layer to $y/ \delta \approx 0.2$. An outer peak in intensity was also evident for the largest pore sizes. Velocity spectra indicate that this outer peak is associated with large-scale structures resembling Kelvin-Helmholtz vortices that have streamwise length scale $2\delta-4\delta$. Skewness profiles suggest that these large-scale structures may have an amplitude-modulating effect on the interfacial turbulence.

We explore the rotational stability of hovering flight. Our model is motivated by an experimental pyramid-shaped object and a computational lambda-shaped analog hovering passively in oscillating airflows; both systems have been shown to maintain rotational balance during free flight. Here, we attach the lambda-shaped flyer at its apex, allowing it to rotate freely akin to a pendulum. We find that the flyer exhibits stable concave-down and concave-up behavior. Importantly, the down and up configurations are bistable and co-exist for a range of background flow properties. We explain the aerodynamic origin of this bistability and compare it to the inertia-induced stability of an inverted pendulum oscillating at its base. We then allow the flyer to flap passively by introducing a rotational spring at its apex. For stiff springs, flexibility diminishes upward stability but as stiffness decreases, a new transition to upward stability is induced by flapping. We conclude by commenting on the implications of these findings for biological and man-made aircraft.

This article accompanies a fluid dynamics video entered into the Gallery of Fluid Motion of the 66th Annual Meeting of the APS Division of Fluid Dynamics., Comment: High and low resolution videos associated with this manuscript can be found as ancillary files