Diffusiophoresis is the movement of colloidal particles due to a gradient in the concentration of a solute. Previous studies on diffusiophoresis have focused largely on one-dimensional colloid transport due to the gradient of a single electrolyte. Recent studies have considered two-dimensional geometries including dead-end pores, multiple electrolytes, and a background flow field due to diffusioosmosis. In this work, we develop a model of the time-dependent diffusiophoretic compaction of colloids in a two-dimensional pore due to the gradient of multiple electrolytes in tandem with a diffusioosmotic slip-driven background flow field, which builds upon these recent studies by combining each of these effects. We simulate this model for varying properties of the pore walls and colloidal particles. Furthermore, we conduct experiments varying the initial ion combinations and total solute concentration, which show good qualitative agreement with the simulations. Our results indicate that diffusiophoretic compaction can be increased or decreased by manipulating electrolyte combinations, total solute concentration, wall charge, and particle diffusivity; each effect can modify the particle velocity, with varying strength, in unison or in opposition to the other effects. By offering a larger toolbox to manipulate colloidal particles, our results on diffusiophoretic and diffusioosmotic motion in tandem and in the presence of multiple electrolytes can be exploited for lab-on-a-chip and biophysics applications.

A composite drag control (CDC) combining the opposition (OC) and spanwise opposed wall-jet forcing (SOJF) methods is studied in a turbulent channel flow via direct numerical simulation of the incompressible Navier-Stokes equations. A maximum drag reduction of about $33\%$ is obtained for CDC—much higher than that produced by either individual method (namely, 19% for SOJF and 23% for OC). Due to the small power input required for both OC and SOJF methods, a significant net power saving (about 32%) is achieved via CDC. Flow analysis shows that CDC can take advantage of both OC and SOJF methods to better suppress drag producing near-wall turbulent structures—vortices and streaks. In particular, due to the presence of the large-scale coherent swirls generated by SOJF, it is more effective than OC in suppressing the random turbulence. Moreover, due to the OC's role in suppressing random small-scale turbulence, CDC requires weaker large-scale coherent swirls than those using SOJF only—hence decreasing the drag contribution associated with large-scale swirls. In summary, our results suggest prospects of employing composite control strategy for effective skin friction drag reduction, particularly at very high Reynolds numbers.

We studied turbulence induced by the Rayleigh-Taylor (RT) instability for two-dimensional (2D) immiscible two-component flows by using a multicomponent lattice Boltzmann method with a Shan-Chen pseudopotential implemented on graphics processing units. We compare our results with the extension to the 2D case of the phenomenological theory for immiscible 3D RT turbulence studied by Chertkov and collaborators [Phys. Rev. E 71, 055301 (2005)]. Furthermore, we compared the growth of the mixing layer, typical velocity, average density profiles, and enstrophy with the equivalent case but for miscible two-component fluid. In both the miscible and immiscible cases, the expected quadratic growth of the mixing layer and the linear growth of the typical velocity are observed with close long-time asymptotic prefactors but different initial transients. In the immiscible case, the enstrophy shows a tendency to grow like $\propto t^{3/2}$, with the highest values of vorticity concentrated close to the interface. In addition, we investigate the evolution of the typical drop size and the behavior of the total length of the interface in the emulsionlike state, showing the existence of a power-law behavior compatible with our phenomenological predictions. Our results can also be considered as a validation step to extend the application of the lattice Boltzmann tool to study the 3D immiscible case.

This study presents a numerical procedure, which we call the macroscopic forcing method (MFM), which reveals the differential operators acting on the mean fields of quantities transported by underlying fluctuating flows. Specifically, MFM can precisely determine the eddy diffusivity operator, or more broadly said, it can reveal differential operators associated with turbulence closure for scalar and momentum transport. We present this methodology by considering canonical problems with increasing complexity. Starting from the well-known problem of dispersion of passive scalars by parallel flows we elucidate the basic steps in quantitative determination of the eddy viscosity operators using MFM. Utilizing the operator representation in Fourier space, we obtain a stand-alone compact analytical operator that can accurately capture the nonlocal mixing effects. Furthermore, a cost-effective generalization of MFM for analysis of nonhomogeneous and wall-bounded flows is developed and is comprehensively discussed through a demonstrative example. Extension of MFM for analysis of momentum transport is theoretically constructed through the introduction of a generalized momentum transport equation. We show that closure operators obtained through MFM analysis of this equation provide the exact RANS solutions obtained through averaging of the Navier-Stokes equation. We introduce MFM as an effective tool for quantitative understanding of non-Boussinesq effects and assessment of model forms in turbulence closures, particularly, the effects associated with anisotropy and nonlocality of macroscopic mixing.

We use large-eddy simulation (LES) to perform a mechanistic study on the momentum transfer between turbulent flows and a traveling wave boundary. Several previous field observations showed that this momentum flux varies with the different wave boundary conditions related to the shoaling effect. In this study, we conduct wall-resolved LES to investigate the canonical problem of turbulence over streamwise traveling wave surfaces with the shoaling effect incorporated. Our result shows that shoaling induces a noticeable difference in the mean profile and the velocity fluctuations of the turbulence field. An analysis on the momentum budget shows that, in the wave boundary layer, the wave-induced momentum flux terms become much higher in the turbulence field as shoaling occurs. By comparison with a third computational case which is used as a control case, we find that the shoaling-induced wave age reduction contributes the most to the enhanced form drag, through the changes in the wave-coherent surface pressure asymmetry and amplitude, while the increased wave steepness also leads to the form drag increase but plays a secondary role. Our result identifies the roles of the wave age and steepness in the shoaling-induced momentum flux increase, which is valuable for the future development of parametrizations. We also observe quasiperiodic large-scale motions, which indicate the correlation between the friction generation and the turbulence self-sustaining process.

In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid-scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term prediction of the underlying chaotic dynamics with our framework compared to using only neural network parametrizations for future prediction. Moreover, we demonstrate that these data-driven parametrization models can handle the non-Gaussian statistics of subgrid-scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular nonintrusive way.

The weights of a deep neural-network model are optimized in conjunction with the governing flow equations to provide a model for subgrid-scale stresses in a temporally developing plane turbulent jet at Reynolds number ${\text{Re}}_0=6000$. The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier-Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered subgrid-scale stresses, without the constraint of being embedded within the flow equations during the training, fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

We study the applicability of tools developed by the computer vision community for feature learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis the capability of convolutional neural networks embedded in a deep generative adversarial model (deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configurations of three-dimensional turbulence in the presence of rotation, a case with multiscale random features where both large-scale organized structures and small-scale highly intermittent and non-Gaussian fluctuations are present. Second, following a reverse engineering approach, we aim to rank the input flow properties (features) in terms of their qualitative and quantitative importance to obtain a better set of reconstructed fields. We present two approaches both based on context encoders. The first one infers the missing data via a minimization of the $L_2$ pixel-wise reconstruction loss, plus a small adversarial penalization. The second, searches for the closest encoding of the corrupted flow configuration from a previously trained generator. Finally, we present a comparison with a different data assimilation tool, based on Nudging, an equation-informed unbiased protocol, well known in the numerical weather prediction community. The TURB-Rot database of roughly 300 K two-dimensional turbulent images is released and details on how to download it are given.

This work presents a review and perspectives on recent developments in the use of machine learning (ML) to augment Reynolds-averaged Navier-Stokes (RANS) and large eddy simulation (LES) models of turbulent flows. Different approaches of applying supervised learning to represent unclosed terms, model discrepancies, and subfilter scales are discussed in the context of RANS and LES modeling. Particular emphasis is placed on the impact of the training procedure on the consistency of ML augmentations with the underlying physical model. Techniques to promote model-consistent training, and to avoid the requirement of full fields of direct numerical simulation data are detailed. This is followed by a discussion of physics-informed and mathematical considerations on the choice of the feature space, and imposition of constraints on the ML model. With a view towards developing generalizable ML-augmented RANS and LES models, outstanding challenges are discussed, and perspectives are provided. While the promise of ML-augmented turbulence modeling is clear, and successes have been demonstrated in isolated scenarios, a general consensus of this paper is that truly generalizable models require model-consistent training with careful characterization of underlying assumptions and imposition of physically and mathematically informed priors and constraints to account for the inevitable shortage of data relevant to predictions of interest. Thus, machine learning should be viewed as one tool in the turbulence modeler's toolkit. This modeling endeavor requires multidisciplinary advances, and thus the target audience for this paper is the fluid mechanics community, as well as the computational science and machine learning communities.

Fish swim by undulating their bodies. These propulsive motions require coordinated shape changes of a body that interacts with its fluid environment, but the specific shape coordination that leads to robust turning and swimming motions remains unclear. To address the problem of underwater motion planning, we propose a simple model of a three-link fish swimming in a potential flow environment and we use model-free reinforcement learning for shape control. We arrive at optimal shape changes for two swimming tasks: swimming in a desired direction and swimming towards a known target. This fish model belongs to a class of problems in geometric mechanics, known as driftless dynamical systems, which allow us to analyze the swimming behavior in terms of geometric phases over the shape space of the fish. These geometric methods are less intuitive in the presence of drift. Here, we use the shape space analysis as a tool for assessing, visualizing, and interpreting the control policies obtained via reinforcement learning in the absence of drift. We then examine the robustness of these policies to drift-related perturbations. Although the fish has no direct control over the drift itself, it learns to take advantage of the presence of moderate drift to reach its target.

The task of dynamic flow estimation is to construct an instantaneous approximation of an evolving flow, and particularly its response to disturbances, using measurements from available sensors. Building from previous work by Darakananda et al. [Phys. Rev. Fluids 3, 124701 (2018)], we further develop an ensemble Kalman filter (EnKF) framework for aerodynamic flows based on an ensemble of randomly perturbed inviscid vortex models of flow about an infinitely thin plate. In the forecast step, vortex elements in each ensemble member are advected by the flow and new elements are released from each edge of the plate; the elements are modestly aggregated to maintain an efficient representation. The vortex elements and leading-edge constraint are corrected in the analysis step by assimilating the surface pressure differences across the plate measured from the truth system. We show that the overall framework can be physically interpreted as a series of adjustments to the position and shape of an elliptical region of uncertainty associated with each vortex element. In this work, we compare the previously used stochastic EnKF with the ensemble transform Kalman filter (ETKF), which uses a deterministic analysis step. We examine the response of the flat plate at ${20}^{\circ }$ in two perturbed flows, with truth data obtained from high-fidelity Navier-Stokes simulation at Reynolds number 500. In the first case, we apply a sequence of large-amplitude pulses near the leading edge of the plate to mimic flow actuation. In the second, we place the plate in a vortex street wake behind a cylinder. In both cases, we show that the vortex-based framework accurately estimates the pressure distribution and normal force, with no a priori knowledge of the perturbations or their structure. We show that, in each case, the ETKF is consistently more robust than the stochastic EnKF and is qualitatively better at representing the coherent structures of the true flow. Finally, we examine the mapping from measurements to state update in the analysis step through singular value decomposition of the Kalman gain.

The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of corotating and/or counterrotating coherent traveling shock waves whose nonlinear mode-locking behavior exhibits bifurcations and instabilities which are not well understood. Computational fluid dynamics simulations are ubiquitous in characterizing the dynamics of the RDE's reactive compressible flow. Such simulations are prohibitively expensive when considering multiple engine geometries, different operating conditions, and the long-time dynamics of the mode-locking interactions. Reduced-order models (ROMs) provide a critically enabling simulation framework because they exploit low-rank structure in the data to minimize computational cost and allow for rapid parametrized studies and long-time simulations. However, ROMs are inherently limited by translational invariances manifest by the combustion waves present in RDEs. In this work, we leverage machine learning algorithms to discover moving coordinate frames into which the data are shifted, thus overcoming limitations imposed by the underlying translational invariance of the RDE and allowing for the application of traditional dimensionality reduction techniques. We explore a diverse suite of data-driven ROM strategies for characterizing the complex shock wave dynamics and interactions in the RDE. Specifically, we employ the dynamic mode decomposition and a deep Koopman embedding to give modeling insights and understanding of combustion wave interactions in RDEs.

This research gauges the ability of deep reinforcement learning (DRL) techniques to assist the optimization and control of fluid mechanical systems. It relies on introducing single-step proximal policy optimization (PPO), a “degenerate” version of the PPO algorithm, intended for situations where the optimal policy to be learnt by a neural network does not depend on state, as is notably the case in open-loop control problems. The numerical reward fed to the neural network is computed with an in-house stabilized finite elements environment implementing the variational multiscale method. Several prototypical separated flows in two dimensions are used as testbed. The method is applied first to two relatively simple optimization test cases (maximizing the mean lift of a NACA 0012 airfoil and the fluctuating lift of two side-by-side circular cylinders, both in laminar regimes) to assess convergence and accuracy by comparing to in-house direct numerical simulation (DNS) data. The potential of single-step PPO for reliable black-box optimization of computational fluid dynamics systems is then showcased by tackling several problems of open-loop control with parameter spaces large enough to dismiss DNS. The approach proves relevant to map the best positions for placement of a small control cylinder in the attempt to reduce drag in laminar and turbulent cylinder flows. All results are consistent with in-house data obtained by the adjoint method, and the drag of a square cylinder at Reynolds numbers in the range of a few thousands is reduced by $30\%$, which matches well reference experimental data available from literature. The method also successfully reduces the drag of the fluidic pinball, an equilateral triangle arrangement of rotating cylinders immersed in a turbulent stream. Consistently with reference machine learning results from the literature, drag is reduced by almost $60\%$ using a so-called boat tailing actuation made up of a slowly rotating front cylinder and two downstream cylinders rotating in opposite directions so as to reduce the gap flow between them.

Wings are used for numerous applications in both air and water and their lift generation in either domain is well understood. However, the lift generated by a wing when it is transitioning out of water and into air has not been quantified to date. This experimental study aims to examine the lift generated by a wing as it performs this water egress. An aspect ratio 4, NACA 0015 wing is translated at constant velocity to investigate the effects of starting depth under the surface, angle of attack, and egress velocity. For all test cases, the wing is translated at constant velocity for at least two chords prior to piercing the surface and the lift profile during the egress is similar for all tested starting depths. The angle of attack affects the time-dependent lift after start and the distance traveled to achieve steady state due to flow attachment changes. However, the angle of attack was not observed to affect the lift profile during egress. The lift history is strongly dependent on egress velocity. Lower velocities register a large lift overshoot followed by a negative lift undershoot before the egress is complete. Higher velocities do not exhibit either overshoot or undershoot and exhibit a more linear transition profile.

The dynamics of finite-span vortex rings expelled from a synthetic jet actuator is studied experimentally using stereoscopic particle image velocimetry as well as being modeled with an inviscid Biot-Savart velocity induction solver. Five rectangular orifices are tested with aspect ratios AR of 2, 4, 6, 13, and 19 at a single actuator stroke length. In the lower synthetic jet, vortex ring axis switching is the dominant factor influencing the jet's shape, while in the upper jet, viscous diffusion plays a more critical role. The variations in the jet's width driven by vortex ring axis switching becomes more extreme with increasing orifice AR. The height of the first axis switch also increases with AR, and for the three lowest AR values tested, the jet axis switches two to three times. However, at orifice AR of 13 and 19, the jet only axis switches once. The lack of additional axis switching is shown to be due to a collision of the vortex ring with itself after the first axis switch and a subsequent bifurcation of the vortex ring. The critical AR limit above which vortex ring bifurcation occurs is found to be consistent with prior work on isolated vortex rings. The axial profiles of centerline velocity for the $\text{AR}=4$–19 jets exhibited two local peaks which become more prominent with increasing jet AR. These variations in centerline velocity are also predicted by the inviscid solver, indicating that they are most likely due to the dynamics of the primary vortex ring and not secondary structures as previously hypothesized.

Microscopic organisms must frequently swim through complex biofluids, including bacterial biofilms and the mucus lining of the upper respiratory tract. Recently, there has been great interest in understanding how the non-Newtonian behavior of the fluids, in particular fluid elasticity, can enable methods of self-propulsion that otherwise would not work in a Newtonian fluid. We present such a swimmer that consists of two spheres of unequal size that rotate in opposite directions. The swimmer is force- and torque-free and placed in an elastic fluid. Using a combination of analytical theory and numerical simulations, we show that this model swimmer, which has zero propulsion in a Newtonian fluid under Stokes flow, swims in the direction of the larger of the two spheres in an elastic fluid. We show that the speed of swimming increases nearly linearly with the Deborah number De or primary normal stress coefficient ${\mathrm{\Psi }}_1$, which is an appropriate measure of the elasticity of the fluid and for $\text{De}\le 1$ is also nearly linear in the concentration of polymer in the fluid. The dependence of the swim speed on the relative size of the two spheres is nonmonotonic, exhibiting a maximum at a size ratio of about 0.75. By analyzing the forces acting on the swimmer and the surrounding flow field, we find that propulsion is driven by thrust due to pressure applied along the swimmer. This thrust originates from flow advection driven by hoop stresses surrounding the faster-spinning smaller sphere. We compare our predictions to experimental measurements of swimming speeds for the bacterium E. coli, which swims via a rotating flagellar bundle and counterrotating body, and find that the speeds predicted by our analysis are remarkably close to the speed increase E. coli experiences in viscoelastic fluids. Finally, we conclude our work by showing how our analysis can be extended to different swimmer configurations and gaits, as long as the propulsion is driven by swirl alone.

We study the effect of surfactant on the pairwise interactions of drops in an applied uniform dc electric field using a combination of numerical simulations based on a boundary integral formulation and an analytical theory assuming small drop deformations. The surfactant is assumed to be insoluble in the bulk-phase fluids. We show that the surfactant weakens the electrohydrodynamic flow, and thus dielectrophoretic interactions play a more prominent role in the dynamics of surfactant-covered drops compared to clean drops. If drop conductivity is the same as the suspending fluid, a nondiffusing surfactant can arrest the drops' relative motion thereby effectively preventing coalescence.

Accretion disks are a ubiquitous phenomenon in astrophysics. To be consistent with observations, there must be an as yet unknown mechanism for angular momentum redistribution. In laboratory experiments, especially, the two-dimensional geometry and the magnetohydrodynamic characteristics of an accretion disk are difficult to reproduce. Here we propose the design of a shallow water experiment in accretion disk geometry, where differential rotation is induced in a quasi-two-dimensional shallow water layer with an open surface that allows direct measurement of the radial and azimuthal fluid dynamics. The effect of the magnetic field is mimicked by established equivalence of magnetohydrodynamic and viscoelastic fluids. We demonstrate radial outwards transport of angular momentum in an accretion disk laboratory experiment. Therefore, the proposed experimental setup can help us to identify the origin of angular momentum redistribution in accretion disks.

An electric field imposed on a bilayer of fluids that are stably stratified in the presence of gravity leads to an instability manifested by interfacial deflections. For the case of a perfect conductor underlying a perfect dielectric, an analytical expression obtained from weak nonlinear analysis shows that sinusoidal deflections can only lead to subcritical breakup. While this expression indicates that there is a transition wave number below which supercritical saturation ought to occur, it can be shown that such wave numbers cannot be geometrically accessed, thus precluding any supercritical saturation to steady waves.

The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasiadiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully developed turbulent conditions using a five-species, chemically reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inlet of the computational domain, both simulations are initiated in the laminar flow region and the flow is let to evolve up to the fully turbulent regime. Modal forcing by means of localized suction and blowing is used to trigger laminar-to-turbulent transition. The high temperatures reached in the near-wall region including the viscous and buffer sublayers activate significant dissociation of both oxygen and nitrogen. This modifies in turn the thermodynamic and transport properties of the reacting mixture, affecting the first-order statistics of thermodynamic quantities. Due to the endothermic nature of the chemical reactions in the forward direction, temperature and density fluctuations in the reacting layer are smaller than in the frozen-chemistry flow. However, the first- and second-order statistics of the velocity field are found to be little affected by the chemical reactions under a scaling that accounts for the modified fluid properties. We also observed that the Strong Reynolds Analogy remains well respected despite the severe hypersonic conditions and that the computed skin friction coefficient distributions match well the results of the Renard-Deck decomposition extended to compressible flows.