Magnetic fields in several astrophysical objects are amplified and maintained by a dynamo mechanism, which is the conversion of the turbulent kinetic energy to magnetic energy. A dynamo that amplifies magnetic fields at scales less than the driving scale of turbulence is known as the fluctuation dynamo. We study the properties of the fluctuation dynamo in supersonic turbulent plasmas, which is of relevance to the interstellar medium of star-forming galaxies, structure formation in the universe, and laboratory experiments of laser-plasma turbulence. Using numerical simulations of driven turbulence, we explore the global and local properties of the exponentially growing and saturated (statistically steady) state of the fluctuation dynamo for subsonic and supersonic turbulent flows. First, we confirm that the fluctuation dynamo efficiency decreases with compressibility. Then we show that the fluctuation dynamo-generated magnetic fields are spatially intermittent and the intermittency is higher for supersonic turbulence, but in both cases the level of intermittency decreases as the field saturates. We also find a stronger back-reaction of the magnetic field on the velocity for the subsonic case as compared to the supersonic case. Locally we find that the level of alignment between vorticity and velocity, velocity and magnetic field, and current density and magnetic field in the saturated stage is enhanced in comparison to the exponentially growing phase for the subsonic case, but only the current density and magnetic field alignment is enhanced for the supersonic case. Finally, we show that both the magnetic field amplification (mainly due to weaker stretching magnetic field lines) and diffusion decreases when the field saturates, but the diffusion is enhanced relative to amplification. This occurs throughout the volume in the subsonic turbulence, but primarily in the strong-field regions for the supersonic case. This leads to the saturation of the fluctuation dynamo. Overall both the amplification and diffusion of magnetic fields are affected by the exponentially growing magnetic fields and thus a drastic change in either of them is not required for the saturation of the fluctuation dynamo.

Plankton constitutes the productive base of aquatic ecosystems and plays an essential role in the global carbon cycle. The impact of hydrodynamic conditions on the biological activity of plankton species can manifest in a variety of different ways, and the understanding of the basic effects due to multiscale complex flows still appears incomplete. Here we consider a predator-prey model of plankton dynamics in the presence of a turbulent flow past an idealized island, to investigate the conditions under which an algal bloom is observed and the resulting patchiness of plankton distributions. By means of direct numerical simulations, we explore the role of the turbulent intensity and of the obstacle shape. In particular, we focus on population variance spectra, and on their relation with the statistical features of the turbulent flow, as well as on the correlation between the spatial distribution of the planktonic species and velocity field persistent structures. We find that both the average biomass and local plankton dynamics critically depend on the relation between advective and biological timescales, confirming and extending previous results obtained in simpler flow settings. We further provide evidence that, in the present system, due to local flow action plankton accumulates in localized filamentary regions. Small turbulent scales are found to impact the statistics of plankton density fields at very fine scales, but the main global features of the population dynamics only weakly depend on the Reynolds number and are also found to be remarkably independent of the geometrical details of the obstacle.

The Richtmyer-Meshkov (RM) instability has long been an interesting subject due to its fundamental significance in scientific research, as well as its crucial role in engineering applications. In this study, the contribution of shock Mach number on the evolution of the RM instability induced by a shock-accelerated square light bubble is investigated numerically. The square bubble is composed of helium gas and the surrounding (ambient) gas is nitrogen. Three cases of incident shock strength are considered: $M_s=1.21$, 1.7, and 2.1. An explicit mixed-type modal discontinuous Galerkin scheme with uniform meshes is employed to numerically solve a two-dimensional system of unsteady compressible Navier-Stokes-Fourier equations. The numerical results show that the shock Mach number plays an important role during the interaction between a planar shock wave and a square light bubble. The shock Mach number causes significant changes in flow morphology, resulting in complex wave patterns, vorticity generation, vortex formation, and bubble deformation. In contrast to low Mach numbers, high Mach numbers produce the larger rolled-up vortex chains, larger inward jet formation, and a stronger mixing zone with greater expansion. The effects of Mach numbers are explored in detail through phenomena such as the vorticity production and evolution of kinetic energy, dissipation rate, and enstrophy. Finally, the Mach number effects on the time variations of the shock trajectories and interface features are comprehensively analyzed.

Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here we investigate the effects of clean and contaminated bubbles driven upward (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient three-dimensional finite-difference-front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a nonlinear equation of state that relates the surface tension to the surfactant concentration. For Newtonian turbulent bubbly flows, the effects of Triton X-100 and 1-pentanol surfactant are examined. It is observed that the sorption kinetics highly affect the dynamics of bubbly flow. A minute amount of Triton X-100 is found to be sufficient to prevent the formation of bubble clusters restoring the single-phase behavior while even two orders of magnitude more 1-pentanol surfactant is not adequate to prevent the formation of layers. For viscoelastic turbulent flows, it is found that the viscoelasticity promotes formation of the bubble wall-layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows, while the addition of small amount of surfactant (Triton X-100) in this system restores the polymer drag reduction resulting in $25\%$ drag reduction for the $\mathrm{Wi}=4$ case.

In this Letter, we will present a physically consistent theory to derive the governing equations of the large eddy simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable simulations of turbulent flows. Therefore, we assume that a coarse-grained fluid element, subsequently called superfluid element, can be locally defined comprising a large number of smaller elementary fluid elements. Then, similar to nonequilibrium molecular dynamics in which the transport equations of an elementary fluid element can be consistently reconstructed from the local collective dynamics of molecules, the transport equations of a superfluid element can be derived from the local collective dynamics of elementary fluid elements. Interestingly, we find: (a) Favre filtering is a physical consistency condition, (b) why Boussinesq's hypothesis in conjunction with eddy viscosity models is commonly employed in LES, and (c) that the LES framework might be more than a numerical turbulence model for computational fluid dynamics.

The path equations are derived to describe the nonlinear evolution of thin jets generated by temperature fronts. An approximate approach is based on the thermal rotating shallow-water model that accounts for the effect of the temperature gradient and uses the variational principle of least action. The dynamics of jets is shown to be effectively described by a nonlinear system of two $(1+1)$-dimensional partial differential equations. Particular solutions are found in the form of a steady-state meandering jet, a cusped jet, and a two-armed spiral.

Membrane filtration is a process of separating particles from fluids. Over time, particles are trapped within the membrane structure and on the membrane surface, forming a cake. In this paper, we develop a mathematical model for the transient blocking dynamics in a concertinaed filtration device composed of angled porous membranes and dead-ends. We examine how the inclusion of particles affects the flow dynamics, and we uncover potential inaccuracies in relying on flux–throughput curves to distinguish between caking and internal blocking dynamics. Moreover, we show that optimal filtration performance strongly depends on both the performance metric and the membrane configuration. Finally, to optimize the use of membrane area, we introduce a method for deriving a nonuniform permeance that ensures constant initial cake growth.

To study turbulent thermal convection, one often chooses a Rayleigh-Bénard flow configuration, where a fluid is confined between a heated bottom plate, a cooled top plate of the same shape, and insulated vertical sidewalls. When designing a Rayleigh-Bénard setup, for specified fluid properties under Oberbeck-Boussinesq conditions, the maximal size of the plates (diameter or area), and maximal temperature difference between the plates, ${\mathrm{\Delta }}_{max}$, one ponders: Which shape of the plates and aspect ratio $\mathrm{\Gamma }$ of the container (ratio between its horizontal and vertical extensions) would be optimal? In this article, we aim to answer this question, where under the optimal container shape, we understand such a shape, which maximizes the range between the maximal accessible Rayleigh number and the critical Rayleigh number for the onset of convection in the considered setup, ${\text{Ra}}_{c,\mathrm{\Gamma }}$. First we prove that ${\text{Ra}}_{c,\mathrm{\Gamma }}\propto (1+c_u{\mathrm{\Gamma }}^{-2})(1+c_{\theta }{\mathrm{\Gamma }}^{-2})$, for some $c_u>0$ and $c_{\theta }>0$. This holds for all containers with no-slip boundaries, which have a shape of a right cylinder, whose bounding plates are convex domains, not necessarily circular. Furthermore, we derive accurate estimates of ${\text{Ra}}_{c,\mathrm{\Gamma }}$, under the assumption that in the expansions (in terms of the Laplace eigenfunctions) of the velocity and reduced temperature at the onset of convection, the contributions of the constant-sign eigenfunctions vanish, both in the vertical and at least in one horizontal direction. With that we derive ${\text{Ra}}_{c,\mathrm{\Gamma }}\approx {\left(2\pi \right)}^4(1+c_u{\mathrm{\Gamma }}^{-2})(1+c_{\theta }{\mathrm{\Gamma }}^{-2})$, where $c_u$ and $c_{\theta }$ are determined by the container shape and boundary conditions for the velocity and temperature, respectively. In particular, for circular cylindrical containers with no-slip and insulated sidewalls, we have $c_u=j_{11}^2/{\pi }^2\approx 1.49$ and $c_{\theta }={\left({\tilde{j}}_{11}\right)}^2/{\pi }^2\approx 0.34$, where $j_{11}$ and ${\tilde{j}}_{11}$ are the first positive roots of the Bessel function $J_1$ of the first kind or its derivative, respectively. For parallelepiped containers with the ratios ${\mathrm{\Gamma }}_x$ and ${\mathrm{\Gamma }}_y$, ${\mathrm{\Gamma }}_y\le {\mathrm{\Gamma }}_x\equiv \mathrm{\Gamma }$, of the side lengths of the rectangular plates to the cell height, for no-slip and insulated sidewalls we obtain ${\text{Ra}}_{c,\mathrm{\Gamma }}\approx {\left(2\pi \right)}^4(1+{\mathrm{\Gamma }}_x^{-2})(1+{\mathrm{\Gamma }}_x^{-2}/4+{\mathrm{\Gamma }}_y^{-2}/4)$. Our approach is essentially different to the linear stability analysis, however, both methods lead to similar results. For $\mathrm{\Gamma }\lesssim 4.4$, the derived ${\text{Ra}}_{c,\mathrm{\Gamma }}$ is larger than Jeffreys' result ${\text{Ra}}_{c,\infty }^J\approx 1708$ for an unbounded layer, which was obtained with linear stability analysis of the normal modes restricted to the consideration of a single perturbation wave in the horizontal direction. In the limit $\mathrm{\Gamma }\to \infty$, the difference between ${\text{Ra}}_{c,\mathrm{\Gamma }\to \infty }={\left(2\pi \right)}^4$ for laterally confined containers and Jeffreys' ${\text{Ra}}_{c,\infty }^J$ for an unbounded layer is about 8.8%. We further show that in Rayleigh-Bénard experiments, the optimal rectangular plates are squares, while among all convex plane domains, circles seem to match the optimal shape of the plates. The optimal $\mathrm{\Gamma }$ is independent of ${\mathrm{\Delta }}_{max}$ and of the fluid properties. For the adiabatic sidewalls, the optimal $\mathrm{\Gamma }$ is slightly smaller than 1/2 (for cylinder, about 0.46), which means that the intuitive choice of $\mathrm{\Gamma }=1/2$ in most Rayleigh-Bénard experiments is right and justified. For the given plate diameter $D$ and maximal temperature difference ${\mathrm{\Delta }}_{max}$, the maximal attainable Rayleigh number range is about 3.5 orders of magnitudes smaller than the order of the Rayleigh number based on $D$ and ${\mathrm{\Delta }}_{max}$. Deviations from the optimal $\mathrm{\Gamma }$ lead to a reduction of the attainable range, namely, as ${log}_{10}\left(\mathrm{\Gamma }\right)$ for $\mathrm{\Gamma }\to 0$ and as ${log}_{10}\left({\mathrm{\Gamma }}^{-3}\right)$ for $\mathrm{\Gamma }\to \infty$. Our theory shows that the relevant length scale in Rayleigh-Bénard convection in containers with no-slip boundaries is $\ell \sim D/\sqrt{{\mathrm{\Gamma }}^2+c_u}=H/\sqrt{1+c_u/{\mathrm{\Gamma }}^2}$. This means that in the limit $\mathrm{\Gamma }\to \infty$, $\ell$ equals the cell height $H$, while for $\mathrm{\Gamma }\to 0$, it is rather the plate diameter $D$.

Clustered contractions are observed in the human small intestine after fatty meals or in patients with gastrointestinal diseases. We investigate flow produced by a cluster of peristaltic contractions propagating along a circular channel for a finite Reynolds number $\mathrm{Re}\sim {10}^2$ and a finite contraction width (wavelength) $\lambda /D\sim 1$. We perform a computational fluid dynamics analysis of a Newtonian liquid using the cumulant lattice Boltzmann method where zero pressure is given to both ends of the channel. We show that clustered contractions cause retrograde flow over the cluster and fluid trapping in the upstream and downstream regions of the cluster. Flow rate is not proportional to the number of peristaltic waves in a cluster, in particular, for large contraction ratio (amplitude). To understand the underlying mechanism, we simulate flow produced by an isolated contraction in channels with different lengths. The magnitude of pressure gradient produced by the isolated contraction does not decrease largely with increasing the channel length, minimizing a decrease in flow rate. When flow rates of clustered contractions with different numbers of waves are plotted as a function of the channel length per wave, the flow rates collapse onto a single curve of each contraction ratio. In addition, the flow rates of the clustered contractions converge to the flow rates of infinitely periodic contractions. We also compare the characteristics of the flow rate for $\mathrm{Re}\sim {10}^2$ and $\lambda /D\sim 1$ to those for $\mathrm{Re}\to 0$ and $\lambda /D\to \infty$.

We report a closed analytical form of two types of linearly unstable rotational equilibria for a planar motion of two hydrodynamically coupled, inertia-free, pusher swimmers in the bulk of a fluid and at a planar, stress-free, fluid interface. Both types correspond to a periodic motion of pushers along circular trajectories with a constant angular velocity in such a way that the distance between the pushers and their relative orientation remain constant. The first orbit type represents the motion along a common circle, when each pusher makes a $35.2^{\circ }$ angle with their relative position vector. In the second type of orbiting, the pushers move along circles of different radii while the orientation vectors of the pushers make $20.{90}^{\circ }$ and $110.{90}^{\circ }$ angles with their relative position vector. The first orbit type is monotonically unstable and the second orbit type is oscillatorily unstable. Next we show that both types of equilibria can be stabilized by self-induced Marangoni flow, generated by two pushers bound to move along a planar liquid-air interface. Neglecting inertia, we couple the motion of pushers with the advection-diffusion equation for the concentration of an insoluble surfactant, produced by the swimmers. The surfactant is assumed to homogeneously decompose at a constant rate. Numerical simulations in the regime of nonzero Peclet number reveal the existence of stable periodic orbits that are directly linked to the unstable equilibria found analytically in the absence of the Marangoni flow.

Direct simulations of two-dimensional channel flow of a viscoelastic fluid have revealed the existence of a family of Tollmien-Schlichting (TS) attractors that is nonlinearly self-sustained by viscoelasticity [Shekar et al., J. Fluid Mech. 897, A3 (2020)]. Here, we describe the evolution of this branch in parameter space and its connections to the Newtonian TS attractor and to elastoinertial turbulence (EIT). At Reynolds number $\mathrm{Re}=3000$, there is a solution branch with TS-wave structure but which is not connected to the Newtonian solution branch. At fixed Weissenberg number, $\mathrm{Wi}$, and increasing Reynolds number from 3000 to 10 000, this attractor goes from displaying a striation of weak polymer stretch localized at the critical layer to an extended sheet of very large polymer stretch. We show that this transition is directly tied to the strength of the TS critical layer fluctuations and can be attributed to a coil-stretch transition when the local Weissenberg number at the hyperbolic stagnation point of the Kelvin cat's eye structure of the TS wave exceeds $\frac{1}{2}$. At $\mathrm{Re}=10000$, unlike 3000, the Newtonian TS attractor evolves continuously into the EIT state as $\mathrm{Wi}$ is increased from zero to about 13. We describe how the structure of the flow and stress fields changes, highlighting in particular a “sheet-shedding” process by which the individual sheets associated with the critical layer structure break up to form the layered multisheet structure characteristic of EIT.

We analyze the behavior of air bubbles freely rising at high Reynolds numbers in a planar thin-gap cell filled with distilled water. The gap thickness of the cell is fixed to $h\simeq 2.8$ mm (or $h\simeq 1$ mm in additional experiments) and its in-plane width $W$ is varied from 2.4 to 21 cm. This allows us to investigate the evolution from unconfined thin-gap situations (i.e., large $W$ and $h\ll W$) controlled by the bubble characteristic lengths (diameter in the cell plane $d>h$ and thickness close to the gap size $h$) to doubly confined situations controlled by the channel dimensions. As the bubble size $d$ increases, and beyond a critical value that depends on $W$, we observe a mean rise velocity of the bubble, $V_b$, lower than that for larger $W$, along with a modification of the bubble shape. The departure occurs for oscillating bubbles of approximate elliptical shape, which becomes closer to circular as the lateral confinement increases. We further investigate how the bubble oscillatory motion is impacted by the transverse confinement. Assuming that the wall effect is related to the strength of the downward flow generated by the bubble, we introduce the relative velocity $U_{\mathrm{rel}}=V_b/\xi$, where $\xi =1-d/W$ is the confinement ratio and found $U_{\mathrm{rel}}\simeq V_{b,\infty }$ for all the cell widths considered, where $V_{b,\infty }$ is the mean rise velocity in the absence of the transverse confinement (i.e., for $W$ sufficiently large). This provides an estimation, at leading order, of the bubble velocity, $V_b\simeq 0.8\xi {(h/d)}^{1/6}\sqrt{gd}$, that generalizes the expression proposed by Filella et al. J. Fluid Mech. 778, 60 (2015) and accounts for the additional drag experienced by the bubble due to the lateral walls. We then show that, for given $d$ and $\xi$, the frequency and amplitudes of the oscillatory motion can be predicted using the characteristic length and velocity scales, $d$ and $U_{\mathrm{rel}}$. As the bubble size is increased further, the bubble behavior becomes fully dominated by the channel dimensions. Cylindrical-capped shapes emerge, corresponding to a radius of curvature $R_c$ at the front of the bubble, $R_c\simeq 0.31W$, independent of the bubble size and of the gap thickness. At the same time, the mean rise velocity of the bubble saturates at a constant value, corresponding to a constant Froude number, $\mathrm{Fr}=V_b/\sqrt{gW}$, that depends on the gap thickness $h$ of the cell.

Pumpless transport of droplets on open surfaces has gained significant attention because of its applications starting from vapor condensation to Lab-on-a-Chip systems. Mixing two droplets on open surfaces can be carried out quickly by using wettability patterning. However, it is quite challenging to split a droplet in the absence of external stimuli because of the interfacial energy of the droplet. Here, we demonstrate a standalone power-free technique for transport and splitting of droplets on open surfaces using continuous wettability gradients. A droplet moves continuously from a low to a high wettability region on the wettability-gradient surface. A Y-shaped wettability-gradient track – laid on a superhydrophobic background – is used to investigate the dynamics of the splitting process. A three-dimensional phase-field Cahn-Hilliard model for interfaces and the Navier-Stokes equations for transport are employed and solved numerically using the finite element method. Numerical results are used to decipher the motion and splitting of droplet at the Y junction using the principle of energy conservation. It is observed that droplet splitting depends on the configuration of the Y junction; droplets split faster for the superhydrophobic wedge angle of ${90}^{\circ }$ and the splitting ratio (ratio of the sizes of daughter droplets) depends on the widths of the Y branches. A critical branch-width ratio ($\frac{w_2}{w_1}=0.79$) is identified below which the droplet does not split and moves towards the branch of higher width and settles there. The present study provides the required theoretical underpinnings to achieve autonomous transport and splitting of droplets on open surfaces, which has clear potential for applications in Lab-on-a-Chip devices.

Implicitly filtered large-eddy simulation (LES) is by nature numerically under-resolved. With the sole exception of Fourier-spectral methods, discrete numerical derivative operators cannot accurately represent the dynamics of all of the represented scales. Since the resolution scale in an LES usually lies in the inertial range, these poorly represented scales are dynamically significant, and errors in their dynamics can affect all resolved scales. This Letter is focused on characterizing the effects of numerical dispersion error by studying the energy cascade in LES of convecting homogeneous isotropic turbulence. Numerical energy and transfer spectra reveal that energy is not transferred at the appropriate rate to wavemodes where significant dispersion error is present. This leads to a deficiency of energy in highly dispersive modes and an accompanying pile up of energy in the well-resolved modes, since dissipation by the subgrid model is diminished. An asymptotic analysis indicates that dispersion error causes a phase decoherence between triad interacting wavemodes, leading to a reduction in the mean energy transfer rate for these scales. These findings are relevant to a wide range of LES, since turbulence commonly convects through the grid in practical simulations. Further, these results indicate that the resolved scales should be defined to not include the dispersive modes.

It is postulated that the pulse modulation of synthetic jet actuators at or close to the natural shedding frequency of a separated flow over an airfoil can control the shedding of vorticity, and thus the load variation exerted onto an airfoil during dynamic stall more effectively than continuous sinusoidal actuation. The forces and flowfields on and around the airfoil were used to determine the mechanism by which pulse-modulated synthetic jet actuators interact with the separated shear layer in both static and dynamic pitch conditions. Both Eulerian and Lagrangian (finite-time Lyapunov exponent) vortex identification techniques were used to identify these interactions. It was shown that pulse modulation can improve many aspects of dynamic stall control with only 35% of the power consumption compared to continuous actuation. Both shallow and deep dynamic stall cases were explored, where the hysteresis in the lift coefficient was reduced when compared to the continuously actuated case. The flowfields during deep dynamic stall showed a dramatic reduction in the size of the wake as compared to the continuously-actuated case when flow separation was present. The Largangian coherent structure analysis described the interaction of the synthetic jet actuators with the separated shear layer at static angles of attack. Analysis of the change in circulation through the wake of the airfoil suggested pulse modulation reduces load excursions by reducing the maximum circulation shed from the suction side during stall inception, and increasing the circulation shed during flow reattachment, leveling out circulation shedding while not mitigating the total circulation, or vorticity, shed. The benefits obtained by utilizing pulse modulation suggest that actuating the synthetic jets with a pulse modulation signal may have a valuable place in the use of these actuators to control dynamic stall, and a mechanism by which this is achieved is proposed.

Reduced models describing the Lagrangian dynamics of the velocity gradient tensor (VGT) in homogeneous isotropic turbulence (HIT) are developed under the physics-informed machine learning (PIML) framework. We consider the VGT at both Kolmogorov scale and coarse-grained scale within the inertial range of HIT. Building reduced models requires resolving the pressure Hessian and subfilter contributions, which is accomplished by constructing them using the integrity bases and invariants of the VGT. The developed models can be expressed using the extended tensor basis neural network (TBNN) introduced by Ling et al. [J. Fluid Mech. 807, 155 (2016)]. Physical constraints, such as Galilean invariance, rotational invariance, and incompressibility condition, are thus embedded in the models explicitly. Our PIML models are trained on the Lagrangian data from a high-Reynolds number direct numerical simulation (DNS). To validate the results, we perform a comprehensive out-of-sample test. We observe that the PIML model provides an improved representation for the magnitude and orientation of the small-scale pressure Hessian contributions. Statistics of the flow, as indicated by the joint PDF of second and third invariants of the VGT, show good agreement with the “ground-truth” DNS data. A number of other important features describing the structure of HIT are reproduced by the model successfully. We have also identified challenges in modeling inertial range dynamics, which indicates that a richer modeling strategy is required. This helps us identify important directions for future research, in particular towards including inertial range geometry into the TBNN.

We develop a mean-field model for an elastic dumbbell that predicts an enhanced concentration of flexible polyelectrolytes in the center of a microfluidic channel due to simultaneous application of axial flow and electric fields. Consistent with previous works, the model indicates that local shear flow stretches and orients a polyelectrolyte molecule so that electrohydrodynamic interactions within the molecule drive its migration towards the center of the channel. Unlike previous works, dispersion due to fluctuations of electrohydrodynamic velocity induced by thermal fluctuations of the molecular configuration is explicitly included in the mean-field model. This electrohydrodynamic dispersion is comparable with or exceeds diffusivity due to Brownian forces for electric field strengths commonly used in microfluidic devices. The developed models are in quantitative agreement with Brownian dynamics simulations and in qualitative agreement with experiments. In particular, competition between the electrohydrodynamic migration and dispersion is shown to cause a nonmonotonic dependence of the polyelectrolyte concentration in the channel center on the magnitude of the electric field.

Natural convection exhibits turbulent flows which are difficult or impossible to resolve in direct numerical simulations. In this work we investigate a quasilinear form of the Rayleigh-Bénard problem which describes the bulk one-dimensional properties of convection without resolving the turbulent dynamics. We represent perturbations away from the mean using a sum of marginally stable eigenmodes. By constraining the perturbation amplitudes, the marginal stability criterion allows us to evolve the background temperature profile under the influence of multiple eigenmodes representing flows at different length scales. We find the quasilinear system evolves to an equilibrium state where advective and diffusive fluxes sum to a constant. These marginally stable thermal equilibria (MSTE) are exact solutions of the quasilinear equations. The mean MSTE temperature profiles have thinner boundary layers and larger Nusselt numbers than thermally equilibrated two- and three-dimensional simulations of the full nonlinear equations. MSTE solutions exhibit a classic boundary-layer scaling of the Nusselt number $\mathrm{Nu}$ with the Rayleigh number $\mathrm{Ra}$ of $\mathrm{Nu}\sim {\mathrm{Ra}}^{1/3}$. When MSTE are used as initial conditions for a two-dimensional simulation, we find that Nu quickly equilibrates without the burst of turbulence often induced by purely conductive initial conditions, but we also find that the kinetic energy is too large and viscously attenuates on a long, viscous timescale.

Swimming organisms can escape their predators by creating and harnessing unsteady flow fields through their body motions. Stochastic optimization and flow simulations have identified escape patterns that are consistent with those observed in natural larval swimmers. However, these patterns have been limited by the specification of a particular cost function and depend on a prescribed functional form of the body motion. Here, we deploy reinforcement learning to discover swimmer escape patterns for larval fish under energy constraints. The identified patterns include the C-start mechanism, in addition to more energetically efficient escapes. We find that maximizing distance with limited energy requires swimming via short bursts of accelerating motion interlinked with phases of gliding. The present, data efficient, reinforcement learning algorithm results in an array of patterns that reveal practical flow optimization principles for efficient swimming and the methodology can be transferred to the control of aquatic robotic devices operating under energy constraints.

Insulator-based dielectrophoresis (iDEP) is an emerging technique for particle manipulation in microfluidic devices. Two nonlinear electrokinetic flows have been demonstrated to take place simultaneously in iDEP: one is induced charge electroosmosis (ICEO) due to the electric polarization of the insulator, and the other is electrothermal flow (ETF) due to the amplified Joule heating of the fluid around the insulator. These flows vary differently with the applied electric field, and become strong in a fluid with a low and a high electric conductivity, respectively. They both exhibit the pattern of fluid vortices near the insulator but with opposite circulating directions. We present in this work an experimental study of the interplay of ICEO and ETF in a constricted microchannel under dc-biased ac voltages. We also develop a depth-averaged numerical model to simulate the coupled electrokinetic fluid flow with the charge and energy transport. The experimentally measured nonlinear fluid velocity agrees closely with the numerical prediction for both a wide range of buffer concentrations and a range of ac voltages. It also matches asymptotically the predicted velocity of ICEO in a low-concentration buffer under a small ac voltage and that of ETF in a high-concentration buffer, both of which are consistent with a scaling analysis. Interestingly, the nonlinear fluid velocity becomes marginal in moderate-concentration buffers under moderate ac voltages because of the opposing effects of ICEO and ETF.