In this paper, we demonstrate a heat transfer mechanism using ultrasonic standing waves. The basic idea behind the proposed heat transfer mechanism is the acoustic relocation phenomenon of inhomogeneous fluid due to acoustic body force. The acoustic body force depends upon the density gradient and the speed of the sound gradient of the inhomogeneous fluid. Heating a fluid creates an inhomogeneity in the physical properties of the fluid such as density, viscosity, and velocity of sound, etc. When this heated (inhomogeneous) fluid is subjected to ultrasonic standing waves, acoustic body force induces a fluid motion which is shown to be responsible for this heat transfer mechanism. Heat transfer enhancement is observed when a standing acoustic wave is passed perpendicular to the direction of heat transfer. Remarkably, it is found that acoustic forces can enhance heat transfer up to 2.5 times compared to natural convection and up to 11.2 times compared to pure conduction. Suppression of natural convection heat transfer is observed when the acoustic waves are passed parallel to the direction of heat transfer. In this case, acoustic forces could bring down the heat transfer by half or more than half from the natural convection. To characterize the heat transfer mechanism in the enhancement case, a modified Rayleigh number that can account for both acoustics and gravity effects is proposed. To this extent, we provide a clear understanding of how acoustic fields influence the fluid flow and heat transfer.

Flow around an oriented cube is experimentally studied using particle image velocimetry measurements. The cube is rigidly suspended and oriented at an angle of ${45}^{\circ }$ with respect to the freestream flow. Instantaneous and mean flow fields in the wake have been examined at 16 different values of Reynolds numbers between 500 and $50000$. Vorticity identified using swirling strength shows a chaotic wake at higher Re. A wider wake and a longer wake length are noted as compared to flow around a normal cube. The wake width collapses to nearly the same value for all Re beyond the wake length. Unlike a cube, an oriented cube has a recirculation region with multiple peaks for velocity deficit, which is a signature of many smaller eddies present in the wake. The range of investigated Reynolds numbers shows behavioral changes in the wake, hinting at the possibility of critical Reynolds numbers (or different regimes) based on a maximum velocity deficit, maximum vorticity magnitude, and energy content of the first mode extracted using proper orthogonal decomposition. Proper orthogonal decomposition has been used to understand the contribution of different modes in the formation of coherent structures in the wake. An oriented cube is an extreme case for nonspherical objects and has marked differences from the wake of a cube and other regular-shaped objects. The present work is an attempt to provide an understanding of and improve upon the scarce investigation performed for the wake of an oriented cube.

Path instability of a millimetric spheroidal bubble in quiescent fluid and in isotropic turbulence is investigated by direct numerical simulation. An immersed boundary method along with a new formulation of the equation of bubble motion is utilized to impose the no-slip condition on the surface of an air bubble in fixed shape with the equivalent diameter of $1.0\sim 4.0\text{mm}$ in contaminated water. The range of Galilei number defined as the ratio of the gravitational force to the kinematic viscosity considered in this study is 100 $\sim$ 800. In still fluid, as the bubble size grows, the frequency of the zigzagging motion of the bubble increases while the range in the orientation angle variation of the bubble is hardly affected. The effect of background turbulence on path instability of a rising bubble, which typically shows zigzag pattern in still fluid, is investigated at three different Reynolds numbers, ${\text{Re}}_{\lambda }$, of 26, 45, and 73, or equivalently, for the ratio of fluid root-mean-square velocity to the bubble rise velocity $u^{\prime }/V_T$ ranging 0.030 $\sim$ 0.671. When a bubble rises in isotropic turbulence, the terminal rise velocity of the bubble does not show a noticeable difference. However, the pathways are significantly distorted by turbulence. Furthermore, the magnitude of zigzagging frequency and the degree of obliquity of the bubble become enhanced with ${\text{Re}}_{\lambda }$. We also observed wakes behind the bubble to find that the rear tails become weaker and tangled due to turbulence.

Nearly 150 years ago, Lord Kelvin proposed the isotropic helicoid, a particle with isotropic yet chiral interactions with a fluid so that translation couples to rotation. An implementation of his design fabricated with a three-dimensional printer is found experimentally to have no detectable translation-rotation coupling, although the particle point-group symmetry allows this coupling. We explain these results by demonstrating that in Stokes flow, the chiral coupling of such isotropic helicoids made out of nonchiral vanes is due only to hydrodynamic interactions between these vanes. Therefore it is small. In summary, Kelvin's predicted isotropic helicoid exists, but only as a weak breaking of a symmetry of noninteracting vanes in Stokes flow.

Some carnivorous mammals (e.g., cats and dogs) lap water with their tongues to drink water at high frequencies. Such a fast moving tongue creates a liquid column out of a bath which is bitten by the mouth for drinking. Presumably, the animals bite just before the pinch-off time of the water column to maximize the water intake. Otherwise, the water column falls back to the bath before being bitten. Such a pinch-off phenomenon in the liquid column can be described as the acceleration-induced (i.e., unsteady) inertia balances with the capillary force. The classical Rayleigh-Plateau instability explains the competition of the steady inertia with the capillarity, but not with the acceleration-induced inertia. In this study, we modify the Rayleigh-Plateau instability in the presence of the fluid acceleration, and show that the most unstable wavenumber and growth rate increase with acceleration. The pinch-off time is theoretically predicted as the $-1/3$ power of the Bond number (i.e, a ratio of the acceleration-induced inertia to capillarity). Finally, measured pinch-off times from previous physical experiments and dog and cat jaw-closing times are shown to be in good agreement with our theoretical pinch-off time. Therefore, our study shows that animals presumably modulate their lapping and jaw-closing time to bite down on the water column before the pinch-off to maximize the water intake.

The small-scale flow structures in a moderately dense turbulent (gas-particle) fluidization are investigated using highly resolved simulation data obtained from a kinetic-theory-based two-fluid model. As a main feature, the invariants of traceless and phase-weighted velocity gradient tensors (rate-of-strain and rate-of-rotation) are computed on the gas and solid phase. The invariant-space joint probability density functions indicate a dominant small-scale topology of tubelike vortical-prevalent clusters and sheetlike viscous dissipative slots on the solid phase. The gas phase, nevertheless, reveals a kind of tendency to a boundary-layer turbulence with a vortex-sheet topology prevalence and balanced mechanism of stretching and contracting enstrophy. From other crucial perspectives, by considering the turbulent interfacial work and drag production [Capecelatro et al., J. Fluid Mech. 780, 578 (2015)], an a priori analysis of the cluster-induced turbulence (pseudo-turbulence) or the subgrid-scale drift velocity parametrizations is outlined. It has been shown that the parametrizations, which depend linearly on the resolved gradient of the solid volume fraction, are invalid in this moderately dense turbulent fluidization. They reveal a clear misalignment with the actual filtered subgrid (solid-induced) drift velocity because of the boundary-layer-like turbulence on gas phase. Alternatively, the tensorial dispersion approach arises to be a valid choice for modeling the drift velocity. The topological analysis, on the other hand, suggests that the linear turbulent dispersion paradigm and the hypothesis of a constant dispersion Prandtl number [Burns et al., ICMF04, (2004), p. 392] is applicable only in the large-scale strain-dominated areas. These and other scrutinies and arguments, from a topological viewpoint, are afforded in this paper.

The flow around a cylinder oscillating in the streamwise direction with a frequency, $f_f$, much lower than the shedding frequency, $f_s$, has been relatively less studied than the case when these frequencies have the same order of magnitude or the transverse oscillation configuration. In this study, particle image velocimetry and the dynamic mode decomposition (DMD) are used to investigate the streamwise-oscillating cylinder wake for forcing frequencies $f_f/f_s\sim 0.04$–0.2 and mean Reynolds number, ${\mathrm{Re}}_0=900$. The amplitude of oscillation is such that the instantaneous Reynolds number remains above the critical value for vortex shedding at all times. Characterization of the wake reveals a range of phenomena associated with the interaction of the two frequencies, including modulation of both the amplitude and frequency of the wake structure by the forcing. DMD reveals a frequency spreading of dynamic modes. A scaling parameter and associated transformation are developed to relate the unsteady, or forced, dynamics of a system to that of an unforced system. For the streamwise-oscillating cylinder, it is shown that this transformation leads to a dynamic mode decomposition similar to that of the unforced system.

The elasto-inertial effects on particle focusing in a square-tube flow were investigated experimentally and numerically. Microscale experiments using spherical particles in dilute polymer solutions demonstrated that the particles are focused on the midline and/or the diagonal in a downstream cross section, depending on the polymer concentration. Numerical computations based on the finitely extensible nonlinear elastic–Peterlin (FENE-P) model for the viscoelastic flow reproduced these focusing patterns. It was revealed that the transitions among the patterns are accounted for by the elastic forces due to the first normal stress difference and the polymer elongation, which are the essentials of the viscoelastic fluid.

The wavelength of undulatory kinematics of fish is an important parameter to determine their hydrodynamic performance. This study focuses on numerical examination of this feature by reconstructing the real physiological model and kinematics of steadily swimming Jack Fish. We perform three-dimensional numerical simulations for flows over these models composed of the trunk, and dorsal, anal, and caudal fins. Moreover, we prescribe the carangiform-like motion for its undulation for a range of wavelengths. Undulation with larger wavelengths improves the hydrodynamic performance of the carangiform swimmer in terms of better thrust production by the caudal fin, lower drag production on the trunk, and reduced power consumption by the trunk. This coincides with the formation of stronger posterior body vortices and leading-edge vortices with more circulation on the caudal fin. The real kinematics of Jack Fish surpasses the performance of those with prescribed motion owing to the flexibility of the caudal fin.

We present a formulation of the physics-informed neural network (PINN) method for learning the effective viscosity of the generalized Newtonian fluid from measurements of velocity and pressure in time-dependent three-dimensional flows and apply it to estimating viscosity models of two non-Newtonian systems (polymer melts and suspensions of particles) in shear flow between two parallel plates using only velocity measurements from numerical simulations. The PINN-inferred viscosity models agree with empirical models for shear rates with large absolute values but deviate for shear rates near zero where empirical models have an unphysical singularity. We show that once the unknown physics is learned the PINN method can be used to solve the momentum conservation equation governing flow of non-Newtonian fluids.

Large-eddy simulation (LES) of turbulence in complex geometries is often conducted using strongly inhomogeneous resolution. The issues associated with resolution inhomogeneity are related to the noncommutativity of the filtering and differentiation operators, which introduces a commutation term into the governing equations. Neglect of this commutation term gives rise to commutation error. While the commutation error is well recognized, it is often ignored in practice. Moreover, the commutation error arising from the implicit part of the filter (i.e., projection onto the underlying discretization) has not been well investigated. Modeling the commutator between numerical projection and differentiation is crucial for correcting errors induced by resolution inhomogeneity in practical LES settings, which typically rely solely on implicit filtering. Here we employ a multiscale asymptotic analysis to investigate the characteristics of the commutator. This provides a statistical description of the commutator, which can serve as a target for the statistical characteristics of a commutator model. Further, we investigate how commutation error manifests in simulation and demonstrate its impact on the convection of a packet of homogeneous isotropic turbulence through an inhomogeneous grid. A connection is made between the commutation error and the propagation properties of the underlying numerics. A modeling approach for the commutator is proposed that is applicable to LES with filters that include projections to the discrete solution space and that respects the numerical properties of the LES evolution equation. It may also be useful in addressing other LES modeling issues such as discretization error.

Rectangular propulsion nozzles offer thrust-vectoring and air-frame-integration advantages over their more commonly studied circular counterparts. However, they display many distinguishing features which violate assumptions, such as azimuthal homogeneity, typically used in prediction tools for circular jets. In the present paper, we examine the utility of an azimuthal Fourier decomposition for rectangular Mach 1.3 jets of aspect ratio (AR) 1, 4, and 8 using large-eddy simulations, with a circular jet of the same equivalent diameter for reference. The simulations manifest key features of rectangular jets, including higher spreading rates and shorter potential cores with increasing AR, axis switching (AR=4), and azimuthal variation in peak acoustic intensity (AR=8). We show that, after projection on a cylindrical frame, a sine-cosine ansatz for the azimuthal Fourier series affords a more convenient representation of nonaxisymmetric flow features than the commonly used complex exponential ansatz. Fluctuation magnitudes of the higher azimuthal modes show rapid reduction in amplitude, similar to those observed in circular jets, especially if an acoustic fluctuation field based on momentum potential theory is chosen instead of pressure fluctuations. The leading modes differ, however, from those of a circular jet in two important aspects, namely, the mechanisms represented by the sine and cosine coefficients of the first azimuthal mode and the rate of streamwise decay of all modes with increasing AR. These differences are traced to the near- and far-field rectangular jet asymmetry by examining azimuthal inhomogeneity, the implications of which are assessed with a generalized expression for acoustic intensity based on energies of leading modes. The significant simplicity of circular plumes is recovered as a special case of the analysis. Invocation of the twofold mirror symmetry property of rectangular jets eases the prediction procedure so that only two extra terms, representing mechanisms unique to rectangular jets, specifically preferential flapping in the minor axis direction and coupling of axisymmetric and second azimuthal modes, are sufficient to recover the advantages of azimuthal decomposition.

The main objective of the present study is the derivation of exact analytical expressions for the orientation and trajectory of a spherical microswimmer submitted to general linear flows and to an external (gravitational or magnetic) force field, a problem known as gyrotaxis or magnetotaxis. We consider linear shear, hyperbolic, solid-rotation, and stagnation flows. The evolution equations of the swimmer orientation and its position are nonlinear and analytical results are the exception rather than the rule. Most available results for cell orientation and trajectories are obtained numerically. The solution for the swimmer orientation is inspired from a method due to Bretherton, initially developed for a different nonlinear equation. We show here that this method can be generalized to our evolution equation. We see that the swimmer under flow exhibits both run (a motion where the orientation angle is kept constant with time) and tumble (the orientation angle is cyclic with time) regimes, and a variety of cell trajectories are extracted analytically, such as parabolic, elliptic, and helical. This study offers a framework to generalize the results to other types of flows.

The reconnection of two interacting vortex tubes is a fundamental process in fluid mechanics, which, at very high Reynolds numbers, is associated with the formation of intense velocity gradients. Reconnection is usually studied using two antiparallel tubes which are destabilized via the long-wavelength Crow instability, leading to a very symmetric configuration and to a strong flattening of the cores into thin sheets. Here, we consider the interaction of two initially straight tubes at an angle of $\beta$ and show that by relaxing some symmetries of the problem, a rich phenomenology appears. When the angle between the two tubes is close to $\beta ={90}^{\circ }$, their interaction leads to pairing of small portions of antiparallel tubes, followed by the formation of thin and localized vortex sheets as a precursor of reconnection. The subsequent breakdown of these sheets involves a twisting of the paired sheets, followed by the appearance of a localized cloud of small-scale vortex structures. By decreasing $\beta$, we show that reconnection involves increasingly larger portions of tubes, whose cores are subsequently destabilizing, leaving behind more small-scale vortices. At the smallest values of the angle $\beta$ studied, the two vortices break down through a mechanism, which leads to a cascadelike process of energy conveyance across length scales similar to what was found for previous studies of antiparallel vortex tubes ($\beta =0$) which imposed no symmetries. While, in all cases, the interaction of two vortices depends on the initial condition, the rapid formation of fine-scale vortex structures appears to be a robust feature, possibly universal at very high Reynolds numbers.

Lipid bilayer membranes have a native (albeit small) permeability for water molecules. Under an external load, provided that the bilayer structure stays intact and does not suffer from poration or rupture, a lipid membrane deforms and its water influx/efflux is often assumed negligible in the absence of osmolarity. In this work we use boundary integral simulations to investigate the effects of water permeability on the hydrodynamics of an inextensible membrane under a mechanical load, such as the viscous stress from an external flow deforming an inextensible membrane in free space or pushing it through a confinement. Incorporating the membrane permeability into the framework of Helfrich free energy for an inextensible, elastic membrane (a vesicle), we illustrate that, in the absence of an osmotic stress gradient, the semipermeable vesicle is affected by water influx/efflux over a sufficiently long time or under a strong confinement. Our simulations quantify the conditions for water permeation to be negligible in terms of the timescales, flow strength, and confinement. These results shed light on how microfluidic confinement can be utilized to estimate membrane permeability.

The dynamics of a neutrally buoyant, eccentric compound drop, suspended in a Poiseuille flow, in the presence of an external temperature gradient have been analyzed here. Assuming the energy and momentum transport to be diffusion-dominated, we derive approximate analytical solutions for the temperature and the velocity fields and subsequently deduce the deformation using asymptotic analysis in bispherical coordinates. We establish that depending on the direction, the presence of an imposed temperature gradient may speed up or slow down the drops. The temperature gradient has a stronger influence on the velocity of the inner drop at different eccentricities, which in turn alters the relative velocity between the drops. As a result, it is possible to achieve equilibrium configurations, where both the drops move with the same velocity. Two such equilibrium configurations exist for temperature gradients beyond a critical limit, one of which is stable. It is revealed that the imposed temperature gradient always increases the deformation as compared to an isothermal flow. Depending on the position of the inner core with respect to the outer drop center and the direction of the applied temperature gradient, the shape of the inner drop may change from prolate to oblate (or vice versa), as it travels within the outer drop. The deformation in the inner drop increases with eccentricity, while the outer drop sees very little deformation even for relatively large capillary numbers.

Using spatiotemporal linear stability theory, we conduct a systematic study of confined countercurrent shear layer velocity profiles, using realistic velocity profiles that capture the effects of wall boundary layers on canonical profile shapes. It is shown, in line with previous studies, that additional unstable modes are generated when confining walls are present. This leads to shifts in the absolute-convective transition boundary, with the effects being dramatic when confinement is on the high-speed side. However, over large parts of the parameter space, as specified by the counterflow parameter $R$ and the degree of confinement ($H$, measured in terms of shear layer momentum thickness), these correspond to long wave modes. It is shown that as counterflow parameter $R$ ($=\frac{U_1-U_2}{U_1+U_2}$, $U_1$ and $U_2$ being primary and secondary velocity streams) is increased to large values, the confined mode gradually decreases in wavelength. Comparisons of the behavior of the frequency of this confined mode are made with observed peak frequencies from the first experimental realization of momentum-driven confined countercurrent shear layers, and the results are shown to be in reasonable agreement.

We numerically investigated steady axisymmetric flow through and around a porous disk with aspect ratio ($\chi$) ranging from 1 to 20, Reynolds number (Re) varying from 10 to 120, and Darcy number (Da) ranging from ${10}^{-6}$ to 1. The wake characteristics are presented in terms of the streamline patterns, the geometrical parameters as well as the occurrence of the recirculating wake. In particular, the bifurcation curves in the Re-Da parametric space can be collapsed onto approximately the same curve for all $\chi$ when the modified $\chi \text{Da}$ is used. Both $\chi$ and Da are demonstrated to be closely related to the drag and have similar effects on the flow behavior. The formation mechanism of recirculating wake at different $\chi$ is further discussed with respect to the base bleed quantified by the flow rate as well as the vorticity accumulation and decay.

Townsend's attached eddy hypothesis (AEH) gives an accurate phenomenological description of the flow kinematics in the logarithmic layer, but it suffers from two major weaknesses. First, AEH does not predict the constants in its velocity scalings, and second, none of the predicted velocity scalings can be obtained from the Navier-Stokes (NS) equations under AEH's assumptions. These two weaknesses separate AEH from more credible theories like Kolmogorov's theory of homogeneous isotropic turbulence, which, despite its phenomenological nature, has one velocity scaling, i.e., $〈\mathrm{\Delta }{u}^3〉=-(4/5)\epsilon r$, that can be derived from the NS equation. Here, $〈\mathrm{\Delta }{u}^3〉$ is the longitudinal third-order structure function, $\epsilon$ is the time-averaged dissipation rate, and $r$ is the displacement between the two measured points. This work aims to address these two weaknesses by investigating the behavior of the third-order structure function in the logarithmic layer of boundary-layer turbulence. We invoke AEH and obtain $〈\mathrm{\Delta }{u}^3〉=D_{3}ln(r/z)+B_3$, where $\mathrm{\Delta }u$ is the streamwise velocity difference between two points that are displaced by a distance $r$ in the streamwise direction, $z$ is the wall-normal location of the two points, $D_3$ is a universal constant, and $B_3$ is a constant. We then evaluate the terms in the Kármán-Howarth-Monin (KHM) equation according to AEH and see if NS equations give rise to a nontrivial result that is consistent with AEH. Last, by resorting to asymptotic matching, we determine $D_3=2.0$ (at sufficiently high Reynolds numbers).

The ultimate goal of a sound theory of turbulence in fluids is to close in a rational way the Reynolds equations, namely, to express the tensor of turbulent stress as a function of the time average of the velocity field. Based on the idea that dissipation in fully developed turbulence is by singular events resulting from an evolution described by the Euler equations, it has been recently observed that the closure problem is strongly restricted, and that it implies that the turbulent stress is a nonlocal function in space of the average velocity field, a kind of extension of classical Boussinesq theory of turbulent viscosity. This leads to rather complex nonlinear integral equation(s) for the time-averaged velocity field. This one satisfies some symmetries of the Euler equations. Such symmetries were used by Prandtl and Landau to make various predictions about the shape of the turbulent domain in simple geometries. We explore specifically the case of the mixing layer for which the average velocity field only depends on the angle of the wedge behind the splitter plate. This solution yields a pressure difference between the two sides of the splitter which contributes to the lift felt by the plate. Moreover, because of the structure of the equations, one can satisfy the Cauchy-Schwarz inequalities for the turbulent stress, also called the realizability conditions. In the limit of small velocity differences between the two merging flows behind the splitter, we predict an angular spreading of the turbulent domain proportional to the square root of the velocity difference, in agreement with experiments.