An emergent property of decaying two-dimensional turbulence is shown to be a weak but persistent statistical heating, or tendency towards clustering of like-signed vortices. The rate of this heating, which is driven by changes to the vortex population due to vortex mergers and straining events, provides a strong constraint on both vortex decay laws and kinetic theories of vortex interactions. A quasi-equilibrium statistical theory determines the energy spectrum from just the vortex interaction energy and bulk information about the number density of the vortices. The emergent heating rate is shown to determine the upscale transfer of energy, and is a powerful constraint on power-law descriptions of the evolving vortex population.

The three-dimensional flow around a spherical clean bubble translating steadily in a wall-bounded linear shear flow is studied numerically. The present work is concerned with the drag and lift forces experienced by the bubble over a wide range of Reynolds number ($0.1\le \text{Re}\le {10}^3$, Re being based on the bubble diameter and relative velocity with respect to the ambient fluid), wall distance ($1.5\le L_{\text{R}}\le 8$, $L_{\text{R}}$ being the distance from the bubble center to the wall normalized by the bubble radius), and relative shear rate ($-0.5\le \text{Sr}\le 0.5$, Sr being the ratio between the velocity difference across the bubble and the relative velocity). Based on the above range of parameters, situations where the bubble is repelled from or attracted to the wall are both covered. The flow structure and vorticity field are analyzed to obtain qualitative insight into the interaction mechanisms at work. The drag and lift forces are computed as well. Their variations agree well with theoretical predictions available in the limit of low-but-finite Reynolds number and, when the fluid is at rest, in the potential flow limit. Numerical results and analytical expressions are combined to provide accurate semiempirical expressions for the drag and lift forces at arbitrary Reynolds number and separation distance.

We study physical mechanisms that trigger transient growth in a high-speed spatially developing laminar boundary layer that interacts with an oblique shock wave. We utilize an approach based on power iteration, with the global forward and adjoint linearized equations, to quantify the transient growth in compressible boundary layers with flow separation. For a Mach 5.92 boundary layer with no oblique shock wave, we show that the dominant transient response consists of oblique waves, which arise from the inviscid Orr mechanism, the lift-up effect, and the first-mode instability. We also demonstrate that the presence of the oblique shock wave significantly increases transient growth over short time intervals through a mechanism that is not related to a slowly growing global instability. The resulting response takes the form of spanwise periodic streamwise elongated streaks, and our analysis of the linearized inviscid transport equations shows that base-flow deceleration near the reattachment location contributes to their amplification. The large transient growth of streamwise streaks demonstrates the importance of nonmodal effects in the amplification of flow perturbations and identifies a route for the emergence of similar spatial structures in transitional hypersonic flows with shock-wave/boundary-layer interactions.

In this study, we investigated the motion of solid particles dispersed in highly viscous complex fluids agitated in a stirred vessel. We used a refractive index matching method and a combination of planar laser-induced fluorescence (PLIF), particle image velocimetry (PIV), and particle-tracking velocimetry (PTV) techniques to measure the velocity fields of the solid and fluid phases simultaneously along with the spatiotemporal distribution of the solids in the tank. The experimental data show that in a Newtonian ambient fluid, particles disperse uniformly in the plane of measurement, while in a strongly shear-thinning viscoelastic ambient fluid they tend to accumulate in the core of the vortices formed in the flow domain. We found that the solids migrate to the core of the vortices also when the ambient fluid is a Boger fluid, i.e., viscoelastic but not shear thinning. The effect of the first normal stress difference, $N1$, on the vortex sizes and circulation intensities was also examined, with both properties decreasing for increasing $N1$. Finally, we observed that the clustering time of the solids in the vessel for viscoelasticity-induced migration was at least three orders of magnitude lower than that obtained from the literature for inertia-induced migration.

We analyze the dynamic behavior of viscoelastic fluids in elastic tubes subject to pulsatile pressure gradients. In particular, we study the dynamic permeability, a response function that relates linearly flow and pressure gradient in frequency domain. We have found resonances that can be associated to the elasticity of the tube and resonances that can be associated to the elasticity of the fluid. There is a rich phenomenology that includes cooperation and competition of both elasticities. Tuning of the system parameters allows for the excitation of the different modes in the system, sometimes giving responses that are larger than the ones of the corresponding systems with elasticity in only one of its elements. This behavior is similar to the one of two coupled oscillators. Our results are relevant for small confining geometries with low Young moduli. For example, for a microtube with a radius of a few hundred microns with the elasticity of polydimethylsiloxane (PDMS), in which a viscoelastic fluid, with the rheological parameters of blood, is driven by a pulsatile pressure gradient, resonance frequencies on the sound range are predicted. In a wide frequency range, the dynamic permeability is much lower than the one of the same fluid flowing in a poly(methyl methacrilate) (PMMA) tube. Our results are potentially useful for tailoring composite laboratory-on-a-chip devices, where introducing materials with different parameters in a device would induce an increase or decrease of the amplitude of the longitudinally averaged flow. We demonstrate that the magnitude of the dynamic permeability for a composite tube, at a given frequency of the driving pressure drop, determines the amplitude of the average flow along the composite tube.

We use large-scale molecular dynamics to study the dynamics at the three-phase contact line in electrowetting of water and electrolytes on no-slip substrates. Under the applied electrostatic potential the line friction at the contact line is diminished. The effect is consistent for droplets of different sizes as well as for both pure water and electrolyte solution droplets. We analyze the electric field at the contact line to show how it assists ions and dipolar molecules to advance the contact line. Without an electric field, the interaction between a substrate and a liquid has a very short range, mostly affecting the bottom, immobilized layer of liquid molecules which leads to high friction since mobile molecules are not pulled towards the surface. In electrowetting, the electric field attracts charged and polar molecules over a longer range, which diminishes the friction.

To identify the mechanism triggering boundary layer transition on a spherical forebody of an Apollo type re-entry capsule direct numerical simulations of perturbed flow are analyzed. The perturbations are generated by deterministic distributed surface roughnesses that resemble model surface imperfections that are mounted on a capsule model and are experimentally investigated in Radespiel et al. [J. Spacecr. Rockets 56, 405 (2019)]. Therein, the role of distributed roughness in the transition scenario was highlighted but the mechanism remained unclear. In this manuscript, the sensitivity of the flow perturbations with respect to the roughness layout is investigated. The great span of spatial scales, i.e., capsule diameter, boundary layer thickness, and micro-size roughness, define the requirements of the numerical method. Modifications to a finite-volume unstructured Cartesian cut-cell method to meet these requirements are presented. The receptivity of the capsule boundary layer to the roughness and the subsequent disturbance growth are analyzed. The roughness properties at the most downstream position govern the flow perturbation. The impact of the streamwise character of the roughness layout is intensified by increasing the Reynolds number of the flow. The growth mechanism is identified as transient growth and the most amplified disturbances are compared to the results of optimal transient growth theory. Streamwise vortices cause growth via the lift-up effect. However, the wall normal scales of optimal and roughness induced disturbance differ significantly leading to suboptimal growth.

Theory is developed to predict the flows induced by small-amplitude two-dimensional vertically propagating internal wave packets under the influence of rotation. While the long-wave response originally predicted by Bretherton [J. Fluid Mech. 36, 785 (1969)] dominates if the influence of background rotation is negligible, the induced waves are found to be evanescent if the Coriolis parameter is sufficiently large. Explicitly, evanescent induced flows dominate if the Coriolis parameter is greater than the forcing frequency, which is set by the ratio of the vertical group velocity of the wave packet divided by the vertical scale of modulation of the wave packet. The predicted structure of the induced flow is confirmed by numerical simulations. For an upward and rightward propagating Gaussian wave packet that dominantly induces a long-wave response, the flow is rightward across the upper flank and leftward across the lower flank of the wave packet. In contrast, the induced flow for a dominantly evanescent response is negative over the middle of the wave packet. This qualitative change in structure is anticipated to influence the modulational stability of moderately large-amplitude wave packets.

We address our long-standing claim that vortex reconnection is one of the dominant sources of aeroacoustic noise in a number of canonical turbulent flows. The reconnection of two antiparallel vortices is studied via direct numerical simulation of the compressible Navier-Stokes equations in order to fully resolve the acoustic noise generation and far-field sound wave propagation. We show that the primary acoustic source is initially located at the contact point and then at the bridges, where reconnected vortex lines accumulate. At the start of reconnection, the sharp near-field pressure rise results in a high level of far-field noise with a clear dipole pattern. As more vortex lines reconnect and recoil from each other by self-induction, the near-field low-pressure zone extends in both the axial and lateral directions, which results in a quadrupole far-field noise. We thus reveal and quantify sound pressure levels and directivity during vortex reconnection. This work paves the way for further investigations of the reconnection generated noise, especially at higher Reynolds numbers.

Water waves in natural environments are typically broadband, nonlinear, and dynamic phenomena. Taking concepts developed for slow light in optics, we address the challenge of designing arrays to control the spatial distribution of wave energy, and amplify specific frequencies from within target frequency bands at individual locations. Meter-scale wave-flume experiments, in which incident waves interact with a chirped array of eight vertical cylinders, demonstrate significant amplifications over a broad frequency range, as predicted numerically and theoretically.

The ciliary locomotion and feeding of an axisymmetric microswimmer in a complex fluid whose viscosity depends on a surrounding nutrient field are investigated numerically in order to extend previous asymptotic results for weak nutrient-viscosity coupling. Numerical simulations capture nonlinearities inherent in the full system that are missed using perturbation-based linearization methods. The microswimmer's ciliary beating is modeled by a slip velocity, i.e., the squirmer model, and body geometry is modeled by spheroids. It is found that swimming speed and feeding are most affected by a nonuniform viscosity environment when the ratio of advection forces to diffusion transport, characterized by the nondimensional Peclét number, is moderate, i.e., $\text{Pe}=O\left(5\right)$. These changes are correlated to significant increases in the pressure force on the surface of the squirmer, as well as differences in power expenditure and hydrodynamic efficiency compared to the constant-viscosity case. Additionally, the swimming and feeding changes are found to be more significant in oblate spheroids than prolate spheroids, although the shape has a smaller effect on performance than Peclét number or surface stroke. These results suggest that nonlocal effects from viscosity variation are caused by a modification to the pressure force, as opposed to the strain rate. These results should be useful in interpreting experiments where a microswimmer affects a fluid's local rheology.

We computationally studied the kinematics of a simple reciprocal model swimmer (asymmetric dumbbell) in a Newtonian fluid as a function of the Reynolds number (Re), and investigated how the onset and gradual increase of inertia impacts swimming behavior: a reversal in the swim direction, flow field, and the swim stroke. We divided the swim stroke into the increase and decrease in the distance between the two spheres (expansion and compression respectively) and related them to power and recovery strokes. We found that the switch in swim direction also corresponds to a switch in power and recovery strokes. We obtained expressions for the mean swimming velocity by collapsing the net displacement during expansion and compression under power-law relationships with respect to Re, the swimmer's amplitude, and the distance between the two spheres. Analyzing the fluid flows, we saw that the averaged flow field during expansion always resembles a pusher and during compression it always resembles a puller, but when averaged over the whole cycle, the flow that dominates is the one that occurs during the power stroke. We also related the power and recovery strokes to the swimming efficiency during times of expansion and compression, and found that the power stroke is, surprisingly, not always more efficient than the recovery stroke. Our results may have important implications in biology and ultimately the design of artificial swimmers.

Natural swimmers usually perform undulations to propel themselves and perform a range of maneuvers. These include various biological species ranging from microsized organisms to large-sized fish that undulate at typical kinematic patterns. In this paper, we consider anguilliform and carangiform swimming modes to perform numerical simulations using an immersed-boundary method based computational solver at various Reynolds number (Re) regimes. We carry out thorough studies using wavelength and Strouhal frequency as the governing parameters for the hydrodynamic performance of undulating swimmers. Our analysis shows that the anguilliform kinematics achieves better hydrodynamic efficiency for viscous flow regime, whereas for flows with higher Re, the wavelength of a swimmer's wavy motion dictates which kinematics will outperform the other. We find that the constructive interference between vortices produced at anterior parts of the bodies and corotating vortices present at the posterior parts plays an important role in reversing the direction of Benard–von Karman vortex street. Since most of the thrust producing conditions appear to cause wake deflection; a critical factor responsible for degrading the hydrodynamic efficiency of a swimmer, we discuss the underlying mechanics that would trigger this phenomenon. Moreover, we also find that resistive thrust force due to the frictional drag for anguilliform swimmers plays a substantial role in their propulsion at a low Reynolds number. As we approach more inertial flow conditions, its role is minimum and our carangiform swimmers primarily takes advantage of the thrust force due to the added mass effect under all the flow and kinematic conditions. Our findings are expected to provide a guideline on their selection for bioinspired underwater vehicles.

Reactive mixing, in which fluid flow affects the dynamics of a chemical or biological process by continually altering local concentrations, is common in industrial systems. Often a key design goal is to generate reaction products as quickly as possible while expending minimal energy to drive the flow. In systems like microfluidic devices, where turbulence is inaccessible, efficient reactive mixing requires choosing flows carefully. Here we compare product generation rates of an autocatalytic reaction in a collection of steady, laminar shear flows, all with the same kinetic energy, to each other and to the case of reaction without flow. The resulting advection-reaction-diffusion dynamics are estimated by tracking reaction fronts using the computationally inexpensive eikonal approximation, then simulated directly; the two approaches agree closely. Prior studies noted that reaction fronts in Poiseuille flow converged over time to steady shapes that advance at constant speed (solitary chemical waves), and we find the same phenomenon in all the flows considered. Observing that solitary waves advance at speeds dependent on flow velocity extrema, we construct an analytic model that accurately predicts their shape and speed from the flow velocity profile and chemical front speed. The model implies that concentrating kinetic energy in a narrow region maximizes product generation, and we validate that prediction with further simulations. We show that in the case of solitary waves with speed zero, the model reproduces prior theoretical, experimental, and numerical studies of frozen fronts. By simulating full advection-reaction-diffusion dynamics, we find that the eikonal approximation predicts the size of the reacted region within a few percent and predicts the converged product generation rate within a few tenths of a percent.

We examine the dynamics of a thin film formed by a distributed liquid source on a vertical solid wall. The model is derived using the lubrication approximation and includes the effects of gravity, upward airflow, and surface tension. When surface tension is neglected, a critical source strength is found below which the film flows entirely upward due to the airflow, and above which some of the flow is carried downward by gravity. In both cases, a steady state is established over the region where the finite source is located. Shock waves that propagate in both directions away from the source region are analyzed. Numerical simulations are included to validate the analytical results. For models including surface tension, further numerical simulations are carried out. The presence of surface tension, even when small, causes a dramatic change in the film profiles and the speed and structure of the shock waves.

Helicity, defined as the inner product of the velocity and the vorticity vector, is elusive to measure even for laminar flows. Theoretical results for turbulence have shown that flow structures of high helicity are associated with low dissipation of kinetic energy, making them candidates for coherent structures that can persist longer than others in the flow field. As scalar transport in turbulence is enhanced by three-dimensional coherent motions, study of helicity could reveal flow structures that contribute more than others to scalar transport. Direct numerical simulations of turbulent channel flow at ${\mathrm{Re}}_{\tau }=300$ in conjunction with Lagrangian tracking of fluid particles and passive scalar markers for Schmidt numbers 0.7 and 200 are used here. Local helicity along the trajectories of these markers and the fluid particles is calculated. Different levels of helicity are found to relate to the probability that these markers will remain inside a coherent region. The Lagrangian helicity distribution is also presented, indicating a change of the alignment between velocity and vorticity vectors for scalar transport markers.

Drag reduction analyses for turbulent flow over a swept flat plate are conducted. To be more precise, large-eddy simulations of oblique traveling transversal surface waves in turbulent flat plate boundary layer flow at a momentum thickness based Reynolds number of ${\text{Re}}_{\theta }=1000$ are performed. For two parameter sets of the actuation parameters wavelength, period, and amplitude the angle between the wave propagation direction and the streamwise direction, i.e., the sweep angle $\phi$, is varied. The goal is to investigate the susceptibility of drag reduction, net power saving, and turbulence to different sweep angles of the traveling waves. The extension of the technique of spanwise traveling transversal surface waves allows partially up- or downstream traveling waves, i.e., opposite to or in the main flow direction. For downstream traveling waves, the periodic spanwise shear is decreased and the reduction of the wall-shear stress is diminished. Nevertheless, strong decreases of the turbulent stress tensor components persist even for the largest sweep angle. For upstream traveling waves, there is an increase of the lowered friction drag reduction. However, the turbulence level in the outer flow is also higher since the pressure drag is increased such that the total drag reduction is massively lowered. Compared to a purely spanwise traveling wave, i.e., $\phi =0^{\circ }$, the sweep angle $\phi \ne 0^{\circ }$ leads to a much stronger phase dependence of the skin friction since the partially up- and downstream traveling waves induce also periodic fluctuations in the streamwise direction. A shift of energy towards larger scale motions is observed which is also reflected by an increase of the integral length scale close to the wall.

We investigate numerically the three-dimensional (3D) flow around a squareback Ahmed body at Reynolds number $\text{Re}={10}^4$. Proper orthogonal decomposition (POD) is applied to a symmetry-augmented database in order to describe and model the flow dynamics. Comparison with experiments at a higher Reynolds number in a plane section of the near wake at midheight shows that the simulation captures several features of the experimental flow, in particular the antisymmetric quasisteady deviation mode. 3D POD analysis allows us to classify the different physical processes in terms of mode contribution to the kinetic energy over the entire domain. It is found that the dominant fluctuating mode on the entire domain corresponds to the 3D quasisteady wake deviation, and that its amplitude is well estimated from 2D near-wake data. The next most energetic flow fluctuations consist of vortex shedding and bubble pumping mechanisms. It is found that the amplitude of the deviation is negatively correlated with the intensity of the vortex shedding in the spanwise direction and the suction drag coefficient. Finally, we find that despite the slow convergence of the decomposition, a POD-based low-dimensional model reproduces the dynamics of the wake deviation observed experimentally, as well as the main characteristics of the global modes identified in the simulation.

In this paper, we study the large-scale structure of decaying homogeneous flows displaying high-density contrasts and small turbulent Mach numbers. Following Batchelor and Proudman [Batchelor and Proudman, The large-scale structure of homogeneous turbulence, Phil. Trans. R. Soc. A 248, 369 (1956)], we draw an analogy between this configuration and that of a single isolated eddy displaying density nonuniformities. By doing so, we are able to highlight the crucial role played by the solenoidal component of the momentum in the preservation of initial conditions. In particular, we show that the large-scale initial conditions of the spectrum of the solenoidal momentum are preserved provided its infrared exponent is smaller than 4. This condition is reminiscent of the one usually derived in constant-density flow, except that it does not apply to the velocity spectrum. The latter is actually shown to be impermanent for infrared exponents larger than or equal to 2. The consequences of these properties on the self-similar decay of the flow are discussed. Finally, these predictions are verified by performing large eddy simulations of homogeneous isotropic turbulence.

We investigate experimentally the formation of the particular ice structure obtained when a capillary trickle of water flows on a cold substrate. We show that after a few minutes the water ends up flowing on a tiny ice wall whose shape is permanent. We characterize and understand quantitatively the formation dynamics and the final thickness of this ice structure. In particular, we identify two growth regimes. First, a one-dimensional (1D) solidification diffusive regime, where ice is building independently of the flowing water. And second, once the ice is thick enough, the heat flux in the water comes into play, breaking the 1D symmetry of the problem, and the ice ends up thickening linearly downward. This linear pattern is explained by considering the confinement of the thermal boundary layer in the water by the free surface.