The ability to impart momentum while maintaining a zero net mass flux renders synthetic jet actuators attractive tools for a wide variety of applications. Implementation of a single synthetic jet actuator for large-scale operations is unrealistic and, as such, an array of actuators is usually desired during flow control processes. The added complexity of several synthetic jets in close proximity and the subsequent jet-jet interaction, in addition to interaction with the cross flow, represent an area of research yet to be fully explored. This paper encompasses a parametric study to investigate the interaction of a zero pressure gradient turbulent boundary layer (${\text{Re}}_{\tau }=1300$) with twin parallel synthetic jets, where the major axis of the rectangular orifices is aligned with the cross flow. Only the separation distance, $s$, and the phase difference, $\beta$, between the two orifices are varied. Geometrical parameters such as the orifice shape and aspect ratio ($\text{AR}=13$), as well as fluidic properties such as the jet Strouhal number ($\text{St}=2.3$) and the momentum coefficient ($C_{\mu }=0.16$) are kept constant throughout. Velocity fields acquired through stereoscopic particle image velocimetry (SPIV) measurements at five downstream locations indicate noticeable differences in the flow field and associated stresses. A limit in spacing is noted beyond which any subsequent increase results in the twin jets behaving as two independent synthetic jets. In comparison to a single synthetic jet in cross flow, the results demonstrate that twin jets operate at a specific phase difference and spacing can be equally, if not, more efficient for flow entrainment and momentum distribution.

We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem iteratively with large ensembles of initial guesses for three canonical boundary conditions—both ends fixed, one end fixed and one free, and both free. Over several orders of magnitude of membrane mass density, we find instability by divergence or flutter (particularly at large mass density or with one or both ends free). The most unstable eigenmodes generally become wavier at smaller mass density and smaller tension but with regions of nonmonotonic behavior. We find good quantitative agreement with unsteady time-stepping simulations at small amplitudes, but only qualitative similarities with the eventual steady-state large-amplitude motions.

Recent research indicates that the structure of the wall-bounded turbulence depends on the mean shear created by the wall. To examine the response of the wall turbulence to the rough-wall-like mean shear, we performed numerical tests of the channel flows in the framework of the constrained large-eddy simulation without resolving the roughness elements. Once the rough-wall-like mean shear is imposed, the normalized contribution of the sweep motions to the Reynolds stress increases in the near-wall region and the two-point correlation of the streamwise velocity in the outer layer is enhanced. The constraint of the rough-wall-like mean shear provides extra resistance just like the surface roughness, which is observed via the decomposition of the skin friction coefficient. All the statistics indicate that the effect of the rough-wall-like mean shear on the turbulent flow is similar to the effect of roughness elements. The large-eddy simulations of the rough-wall flows using the conventional equilibrium-wall model are also performed for comparison. The statistical results in the outer layer are qualitatively consistent with those obtained by constraining the mean shear, which demonstrates the latter approach can be used as a new wall model for the simulation of the rough-wall flows.

The presence of mean velocity gradients induces anisotropies in turbulent flows, which affect even the smallest scales of motion at finite Reynolds numbers. By performing direct numerical simulations of the Navier-Stokes equations, we study the return to isotropy of a homogeneous turbulent flow initially in a statistically stationary state under a uniform shear, $S=\frac{\partial U_1}{\partial x_2}$, in the conceptually simple situation where the mean shear is suddenly released. In particular, we characterize the timescales involved in the dynamics. We observe that the Reynolds stress tensor, which measures the large-scale flow anisotropy, relaxes towards an isotropic form over a timescale of the order of the large-eddy turnover time of turbulence, in qualitative agreement with previous studies with different types of initially imposed mean velocity gradient. We also investigate how the correlations of the velocity gradient tensor relax to isotropy with time. In particular, we focus on the properties of the one-point vorticity correlations $\langle {\omega }_i{\omega }_j\rangle$ and $\langle {\omega }_i{\omega }_j{\omega }_k\rangle$. The nonzero off-diagonal term of the second-order correlation tensor, i.e., the correlation between the streamwise and the transverse components of vorticity, $\langle {\omega }_1{\omega }_2\rangle$, decreases towards 0 over a time of the order of the Kolmogorov timescale. In comparison, the anisotropies in the diagonal components $\langle {\omega }_i^2\rangle$ ($i=1$, 2, or 3) relax over a time significantly longer than the Kolmogorov timescale. This difference can be explained by an elementary theoretical analysis of the dynamics of the anisotropy tensor $b_{ij}^{\omega }\equiv \frac{\langle {\omega }_i{\omega }_j\rangle }{\langle {\omega }_k{\omega }_k\rangle }-\frac{1}{3}{\delta }_{ij}$ at the instant when the shear is released. We also observe that the skewness of the spanwise component of vorticity, $S_{{\omega }_3}$, relaxes slowly towards zero. The relaxation of a small-scale quantity over a time much longer than the Kolmogorov timescale, as surprising as it may seem, is in fact consistent with a known relation between velocity-gradient correlations and the pressure-rate-of-strain correlation, and raises the important question of separation between the timescales characterizing the return to isotropy at large and small scales.

Inviscid computations are presented of a self-propelled virtual body connected to a combined heaving and pitching foil that uses continuous and intermittent motions. It is determined that intermittent swimming can improve efficiency when the dimensionless heave ratio is $h^{*}<0.7$ while it degrades efficiency for $h^{*}\ge 0.7$. This is a consequence of the physical origins of the force production for pitch-dominated $(h^{*}<0.5)$ and heave-dominated $(h^{*}>0.5)$ motions. Based on insight derived from classic unsteady thin airfoil theory, it is discovered that pitch-dominated motions are driven by added mass-based thrust production where self-propelled efficiency is maximized for high reduced frequencies, while heave-dominated motions are driven by circulatory-based thrust production where self-propelled efficiency is maximized by low reduced frequencies. Regardless of the dimensionless heave ratio, the reduced frequency is high for small amplitude motions, high Lighthill numbers, and low duty cycles and vice versa. Moreover, during intermittent swimming, the stopping vortex that is shed at the junction of the bursting and coasting phases becomes negligibly weak for $h^{*}<0.5$ and small amplitude motions of $A^{*}=0.4$. This study provides insight into the mechanistic trade-offs that occur when biological or bioinspired swimmers continuously or intermittently use combined heaving and pitching hydrofoils.

Spatial regions that do not mix effectively with their surroundings and, thus, contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-Bénard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CSs) which we investigate here in direct numerical simulations in convection cells with a square cross section of aspect ratio $\mathrm{\Gamma }=16$, Rayleigh number $\mathrm{Ra}={10}^5$, and Prandtl numbers $\mathrm{Pr}=0.1,0.7$, and 7. The analysis is based on $N=524288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the detected CSs contribute by a third less to the global turbulent heat transport for all investigated Prandtl numbers compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.

Thin-film flow down a vertical fiber gives rise to a number of instabilities that define the bead-on-fiber morphology including Plateau-Rayleigh breakup, isolated bead formation, and convective instabilities. Experiments are performed that reveal an asymmetric instability which depends upon the liquid surface tension and fiber diameter and exhibits all the bead-on-fiber morphologies. The bead dynamics are described by the bead spacing and bead velocity, with the asymmetric morphology displaying more regular dynamics than the symmetric morphology. For the asymmetric morphology, the transition from the Plateau-Rayleigh to convective regime agrees well with predictions for a free viscous jet, indicating a minimal effect between the thin film and fiber. In addition, the dimensionless bead velocity is shown to scale with the capillary number for all experimental data. These observations for the asymmetric bead dynamics can be used as a design tool for heat and mass transfer applications.

We present a general strategy to unify wall-resolved and wall-modeled large-eddy simulation (LES) approaches for turbulent wall-bounded compressible flows. The proposed technique allows one to impose the proper wall stress and heat flux, preserving the no-slip and the isothermal and adiabatic conditions for the velocity and temperature fields, respectively. The approach results in a minimal intrusive algorithm that automatically switches between wall-resolved and wall-modeled LES according to the local near-wall resolution. The methodology is discussed and implemented in a flow solver based on high-order finite difference schemes, the application of which in the context of wall-modeled LES has been less explored in the available literature. Numerical simulations of canonical turbulent channel flow and spatially evolving boundary layer are performed in a wide range of Mach and Reynolds numbers. The results highlight the ability of the present method to accurately reproduce the outer layer turbulent dynamics, with a minimal influence of the near-wall grid resolution. In particular, velocity statistics and two-point spatial correlations are in good agreement with reference direct numerical simulation and wall-resolved LES, confirming the potential of the proposed approach for predictive analysis of wall-bounded flows at high-Reynolds number.

Depositing and obtaining a liquid film of uniform thickness is a problem integral to numerous applications and requires an understanding of capillary leveling, Marangoni flows, evaporation, and various other phenomena. These applications often demand multilayer films where each layer has distinct properties, and this gives rise to additional challenges. It has been experimentally demonstrated that two-layer films in which the layers are miscible can undergo dewetting, but theoretical understanding of this phenomenon is lacking. Through a lubrication-theory-based model, this work studies the mechanisms that may initiate dewetting in miscible two-layer two-component films. The model film consists of nonvolatile solvent and solute with constant density and viscosity. Two coupled fourth-order nonlinear partial differential equations describing the time evolution of the film height and solute concentration are derived and then solved with a pseudospectral method. It is found that a disparity in initial solute concentration between the film layers drives flows that lead to significant film-height nonuniformities. A parametric study is conducted to examine the influence of system parameters on this behavior and to develop several scaling relations that shed light on the underlying physical mechanisms.

Acceleration of particle settling in inclined containers, known as the Boycott effect, is a common natural phenomenon, which can significantly affect the particle conveying process. Particularly for proppant transport constrained in narrow channels, physical mechanisms related to this effect remain undetermined. In this study, an Eulerian-Lagrangian method, i.e., the unresolved computational fluid dynamics–discrete element method, has been adopted to simulate the particle settling process in inclined narrow channels, with an aim to deepen the understanding of the Boycott effect on proppant settling. The simulation results illustrate that two types of granular-induced instabilities dominate the sediment settling process in inclined fractures, which are analogous to Kelvin-Helmholtz instability and Rayleigh-Taylor instability, respectively. Due to the instabilities, spatial inhomogeneity of the particle phase, i.e., particle clustering, is clearly observed. Based on parametric studies, it is proven that there exists a critical inclination angle where the acceleration ratio reaches a maximum, which ranges from 2 to 6 in this work. Moreover, the critical angle can shift between 60 ° and 75 ° as physical properties change, such as fluid viscosity, particle size, and particle density.

Using molecular dynamics simulations we investigate the shear-induced rotational dynamics of a Brownian nanographene (hexabenzocoronene) freely suspended in a liquid. We demonstrate that, owing to a finite hydrodynamic slip at the molecular surface, these flat molecules tend to align with a constant orientation angle instead of performing the classical periodic orbits predicted by Jeffery's theory. Results are extracted for different Péclet numbers and compared to the predictions by a theory developed for a rigid axisymmetric particle with orientation confined to the flow-gradient plane. The theory is based on the resolution of a one-dimensional Fokker-Planck equation for the angle $\phi$ made by one of the particle's diameters with the flow direction. Remarkably, our results show that the essential features of the three-dimensional orientational statistics of the nanographene are captured by the one-dimensional model, given that the hydrodynamic velocity is closed in terms of the slip length $\lambda$. Finally, we explore the situation in which multiple nanographenes are suspended in the liquid, and show that slip results in a reduction in specific viscosity.

This paper investigates the effects of approach flow conditions on the unsteady three-dimensional wake characteristics of a square-back Ahmed body using improved delayed detached eddy simulations. Two approach flow conditions were investigated: a reference uniform flow (case A) and a thick turbulent boundary layer (TBL) (case B), where the Ahmed body is fully submerged in the TBL, $\delta >H$, where $\delta$ is the boundary layer thickness and $H$ is the total height of the body from the ground. Case A is studied extensively in the literature, whereas case B is less studied. The present results showed that the wake structure of case B is significantly different from that of case A. In particular, the wake of case A is dominated by a strong downwash flow from the top surface, but case B exhibits a much stronger upwash flow, which is induced by lower momentum of the fluid that emanates from the ground clearance and the pressure imbalance generated behind the body. For case A, conditional averaging of the flow field based on the sign of the drift force demonstrated the occurrence of the well-known wake switching (bimodality) event in the spanwise direction. However, the bimodality was completely suppressed in the wake of the Ahmed body submerged in the TBL. Both time-averaged turbulence statistics such as the Reynolds stresses and production terms, and time-resolved statistics including spectral analysis and temporal cross correlations are used to explore the differences between the wake structure of the Ahmed body in a uniform flow and thick TBL.

The flow of viscoelastic polymeric fluids through porous media is common in industrial applications such as oil recovery and groundwater remediation. Polymeric stresses can lead to an elastic-induced instability of the flow. Here, we numerically study the flow of a polymeric fluid in a channel consisting of multiple diverging and converging physical constraints, mimicking the pore bodies and throats of an ordered porous medium. Inertial stresses here are negligible, and instead the flow is dominated by elasticity and viscosity; their relative effects are characterized by the Weissenberg number. There is a critical Weissenberg number below which eddies appear on the top and the bottom of each pore. Above the critical Weissenberg number, eddies form in different regions of the pores and multiple distinct unstable flow structures occur. The stretched polymeric chains inside the pore facilitate eddy formation, whereas relaxed chains lead to eddy-free regions. We quantify the eddy area and correlations between the flow patterns of different pairs of pores, as well as polymeric stress and pressure drop across the tortuous channel to better understand the mechanism behind the observed flow patterns.

Despite the apparent complexity of turbulent flow, identifying a simpler description of the underlying dynamical system remains a fundamental challenge. Capturing how the turbulent flow meanders among unstable states (simple invariant solutions) in phase space, as envisaged by Hopf [Commun. Pure Appl. Math. 1, 303 (1948)], using some efficient representation offers the best hope of doing this, despite the inherent difficulty in identifying these states. Here, we make a significant step toward this goal by demonstrating that deep convolutional autoencoders can identify low-dimensional representations of two-dimensional turbulence which are closely associated with the simple invariant solutions characterizing the turbulent attractor. To establish this, we develop latent Fourier analysis that decomposes the flow embedding into a set of orthogonal latent Fourier modes which decode into physically meaningful patterns resembling simple invariant solutions. The utility of this approach is highlighted by analyzing turbulent Kolmogorov flow (monochromatically forced flow on a 2D torus) at $\text{Re}=40,$ where, in between intermittent bursts, the flow resides in the neighborhood of an unstable state and is very low dimensional. Projections onto individual latent Fourier wavenumbers reveal the simple invariant solutions organizing both the quiescent and bursting dynamics in a systematic way inaccessible to previous approaches.

Investigation of the behavior of various types of tsunami wave trains entering bays is of practical importance for coastal hazard assessments. Furthermore, a mathematical algorithm for quick analysis of the run-up in bays for a large number of incident wave scenarios is also a practical need for tsunami hazard assessments. The linear shallow water equations admit two types of solutions inside an inclined bay with parabolic cross sections: energy-transmitting modes and modes with spatial decay towards the inland tip of the bay. In the low-frequency limit there is only one mode susceptible of transmitting energy to the inland tip. A full solution for the run-up requires taking into account these two types of modes and the scattered field outside, leading to mathematical complications. However, in the long wave limit, this complication can be avoided if one imposes the free surface at the bay mouth being equal to twice the disturbance associated with the incident wave in the open sea. The run-up produced by the solution obtained from this Dirichlet boundary condition can be easily calculated using a series of images. In this model no energy is allowed to escape from the bay; therefore the error arising from the simplification of the boundary condition at the bay mouth grows with time. Nevertheless the maximum run-up occurs before this error becomes significant. If the standard deviation of a Gaussian-shaped incident wave is 8 times the square root of the width of the bay, then this simple solution overestimates the first maximum of the run-up only by 12% compared to the exact solution calculated by means of an integral equation. This overestimation is partly due to the fact that the Dirichlet boundary conditions violate the continuity of the fluxes at the bay mouth. The solution associated with the Dirichlet boundary condition is perturbed in order to match fluxes inside and outside of the bay. The height of the first maximum of the run-up coming from the perturbation theory is in excellent agreement with the “exact” solution. This perturbation theory can also be applied to narrow bays with an arbitrary cross section as long as their depth does not change significantly in the longitudinal direction. The method developed here can also be used to calculate maximum run-up in noninclined bays of arbitrary cross section.

The article discusses the numerical simulation of swimming dynamics of a one-dimensional flexible filament in inviscid conditions using the discrete vortex method (DVM). The DVM is used to reduce the computational cost of mesh generation in these types of unsteady problems. To mimic the anguilliform mode of swimming, we have applied the relevant kinematics in the flexible filament motion. Various parameters like wavelength, tail oscillation amplitude, amplitude growth factor, and frequency were varied to quantify the coefficient of thrust and swimming efficiency. For the ranges of parameters covered in our simulations, we identified the boundary between the drag regime and the thrust regime. Further, the role of tail oscillation amplitude with Strouhal number on the transition from the drag to thrust regime is examined. We showed that the wake vortices assume a Bénard–von Kármán (BvK) configuration in the drag producing regime and rearranges to reverse Bénard–von Kármán (rBvK) configuration in the thrust producing regime. The resultant wake vortex distribution, contour map, and associated velocity field are presented to clarify the differences between BvK in the drag regime, axisymmetric vortex distribution in the vicinity of the transition regime of drag and thrust regimes, and rBvK in the thrust regime. Thus, we have identified the optimum parameter regimes to obtain high thrust or achieve swimming efficiency of two-dimensional (2D) flexible filaments. Finally, we believe our numerical simulations can be extended to elucidate the wake vortice's dynamics of flexible filaments in 2D flows or pitching motion of rigid airfoils in quasi-2D flows.

The dynamics of fluids deep in stellar interiors is a subject that bears many similarities with geophysical fluid dynamics, with one crucial difference: the Prandtl number. The ratio of the kinematic viscosity to the thermal diffusivity is usually of order unity or more on Earth, but is always much smaller than one in stars. As a result, viscosity remains negligible on scales that are thermally diffusive, which opens the door to a whole new region of parameter space, namely, the turbulent low Péclet number regime (where the Péclet number is the product of the Prandtl number and the Reynolds number). In this review, I focus on three instabilities that are well known in geophysical fluid dynamics and have an important role to play in stellar evolution, namely, convection, stratified shear instabilities, and double-diffusive convection. I present what is known of their behavior at low Prandtl number, highlighting the differences with their moderate and high Prandtl number counterparts.

Using long-time direct numerical simulations, we analyze the reversals of the large scale zonal flow in two-dimensional Rayleigh-Bénard convection with a rectangular geometry of aspect ratio $\mathrm{\Gamma }$. We impose periodic and free-slip boundary conditions in the streamwise and spanwise directions, respectively. As Rayleigh number Ra increases, large scale flow dominates the dynamics of a moderate Prandtl number fluid. At high Ra, transitions are seen in the probability density function (PDF) of the largest scale mode. For $\mathrm{\Gamma }=2$, the PDF first transitions from a Gaussian to a trimodal behavior, signifying the emergence of large scale flow reversals, where the flow fluctuates between three distinct states: two states in which a zonal flow travels in opposite directions and one state with no zonal mean flow. Further increase in Ra leads to a transition from a trimodal to a unimodal PDF which demonstrates the disappearance of the zonal flow reversals. On the other hand, for $\mathrm{\Gamma }=1$, the zonal flow reversals are characterized by a bimodal PDF of the largest scale mode, where the flow fluctuates only between two distinct states with zonal flow traveling in opposite directions.

We present results of torque and velocity measurement of a 40-cm spherical Couette flow experiment with rough boundaries and compare them with previous work done for smooth boundaries. Spherical Couette flows in liquid metals are a suitable candidate for generating magnetic dynamo states in the laboratory. However, previous work in our 3-m spherical Couette flow experiment and numerical simulation have shown that an enhancement of the poloidal flows and the helicity are likely required to lower the threshold to achieve dynamo action. Finke and Tilgner [Phys. Rev. E 86, 016310 (2012)] suggested roughening the inner sphere boundary by adding baffles in order to achieve these goals. We perform hydrodynamic studies of the effect of three baffle designs: straight (symmetric) and two types of chevronlike (asymmetric) baffles. In addition, we test the effect of baffle height with two variants: 5% and 10% radius height. We observe important differences in the dimensionless torque as a function of the Reynolds and Rossby numbers for these different configurations and explore an asymmetry in the torque with asymmetric baffles. Velocity measurements in both the equatorial and the meridional planes show an effective enhancement of the equatorial jet and the poloidal flows when adding baffles and two different flow topologies for asymmetric baffles in concordance with the torque measurements. Results point to one of the chevronlike baffle designs as a promising upgrade that we will use in our 3-m experiment to effectively increase our chances of obtaining dynamo action.

We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the equilibrium properties of the droplet as its size is changed, observing the emergence of a hierarchy of bifurcations that strongly depends on the particular underlying chemical pattern. Symmetric and periodic patterns lead to a sequence of pitchfork and saddle-node bifurcations that make stable solutions become saddle nodes. Under dynamic conditions, this change in stability suggests that any perturbation in the system can make the droplet shift laterally while relaxing to the nearest stable point, as is confirmed by numerical computations of the Cahn-Hilliard and Navier-Stokes system of equations. We also consider patterns with an amplitude gradient that creates a set of disconnected stable branches in the solution space, leading to a continuous change of the droplet's location upon evaporation.