We test the ability of a low-dimensional turbulence model to predict how dynamics of large-scale coherent structures such as convection rolls change in different cell geometries. The model consists of stochastic ordinary differential equations, which were derived from approximate solutions of the Navier-Stokes equations. We test the model using Rayleigh-Bénard convection experiments in a cubic container, in which there is a single convection roll known as the large-scale circulation (LSC). The model describes the motion of the orientation ${\theta }_0$ of the LSC as diffusion in a potential determined by the shape of the cell. The model predicts advected oscillation modes, driven by a restoring force created by the noncircular shape of the cell cross section. We observe the corresponding lowest-wave-number predicted advected oscillation mode in a cubic cell, in which the LSC orientation ${\theta }_0$ oscillates around a corner, and a slosh angle $\alpha$ rocks back and forth, which is distinct from the higher-wave-number advected twisting and sloshing oscillations found in circular cylindrical cells. Using the Fokker-Planck equation to relate probability distributions of ${\theta }_0$ to the potential, we find that the potential has quadratic minima near each corner with the same curvature in both the LSC orientation ${\theta }_0$ and slosh angle $\alpha$, as predicted. To quantitatively test the model, we report values of diffusivities and damping timescales for both the LSC orientation ${\theta }_0$ and temperature amplitude for the Rayleigh number range $8\times {10}^7\le \text{Ra}\le 3\times {10}^9$. The new oscillation mode around corners is found above a critical $\mathrm{Ra}=4\times {10}^8$. This critical Ra appears in the model as a crossing of an underdamped-overdamped transition. The natural frequency of the potential, oscillation period, power spectrum, and critical Ra for oscillations are consistent with the model if we adjust the model parameters by up to a factor of 2.9, and values are all within a factor of 3 of model predictions. However, these uncertainties in model parameters are too large to correctly predict whether the system is in the underdamped or overdamped state at a given Ra. Since the model was developed for circular cross sections, the success of the model at predicting the potential and its relation to other flow properties for a square cross section—which has different flow modes than the circular cross section—suggests that such a modeling approach could be applied more generally to different cell geometries that support a single convection roll.

Ultrasound is known to enhance surface bubble growth and removal in catalytic and microfluidic applications, yet the contributions of rectified diffusion and microstreaming phenomena toward mass transfer remain unclear. We quantify the effect of ultrasound on the diffusive growth of a single spherical ${\mathrm{CO}}_2$ bubble growing on a substrate in supersaturated water. The time-dependent bubble size, shape, oscillation amplitude, and microstreaming flow field are resolved. We show and explain how ultrasound can enhance the diffusive growth of surface bubbles by up to two orders of magnitude during volumetric resonance. The proximity of the wall forces the bubble to oscillate nonspherically, thereby generating vigorous streaming during resonance that results in convection-dominated growth.

We present a comparison of different particles' velocity and acceleration statistics in two paradigmatic turbulent swirling flows: the von Kármán flow in a laboratory experiment and the Taylor-Green flow in direct numerical simulations. Tracers, as well as inertial particles, are considered. Results indicate that, in spite of the differences in boundary conditions and forcing mechanisms, scaling properties and statistical quantities reveal similarities between both flows, pointing to new methods to calibrate and compare models for particles dynamics in numerical simulations, as well as to characterize the dynamics of particles in simulations and experiments. The comparison also allows us to identify contributions of the mean flow to the inertial-range scaling of the particles' velocity structure functions.

The Leidenfrost effect, classically associated with drops levitating on their own vapor over hot solid surfaces, can also be observed over hot baths of nonvolatile liquids. In view of substrate fluidity, heat transfer through the bath to the drop should most certainly be dominated by convection and not by only conduction as in the solids, which may be instrumental for an efficient heat supply to the drop given typically poor thermal conductivity of the liquids. Here, we undertake an experimental and numerical study of the flow in a bath of silicone oil V20 induced by an overlying Leidenfrost drop, highlighting that a toroidal vortex is formed underneath the drop whose direction of circulation turns out to be different for drops of different liquids. We show that this is due to a shift in a delicate interplay between three mechanisms pulling in different directions: (i) shear stresses exerted by the vapor escaping from the gap between the bath and the drop, as well as (ii) buoyancy action and (iii) thermocapillary (Marangoni) stresses, both due to local evaporative cooling of the bath by the drop. Whatever the structure of this locally induced convection, its crucial heat transfer enhancing efficiency is readily confirmed in numerical simulations as favoring levitation.

We quantify the transient deformation and breakup of a conducting drop suspended in a dielectric medium and subjected to a fluctuating electric field. Specifically, the magnitude of the field fluctuates randomly in time, while its orientation is fixed. Hence, the deformation of the drop is axisymmetric about the direction of the field. The temporal fluctuations are described by a stationary Markovian Gaussian process, characterized by a mean, variance, and correlation time. Small deformation theory predicts that the fluctuations produce a larger deformation than under a steady electric field of strength equal to the mean of the fluctuating electric field. Next, we utilize boundary integral computations to quantify the deformation and breakup of drops beyond the small deformation regime. When the mean of the fluctuating field is greater than the critical field for breakup under a steady field, we find that the average time taken to undergo breakup is less than that under an equivalent steady field. More interestingly, a certain fraction of drops are observed to undergo breakup even when the mean field is less than the critical field. The fraction of drops undergoing breakup and the range of mean electric field below the critical where breakup is observed depends on the strength of fluctuations of the electric field. An operating map is presented for the percentage of drops undergoing breakup as a function of the dimensionless mean field for different strength of field fluctuations. The present study sheds light on the response of drops in applications such as electrocoalescence and electroemulsification, where interactions with surrounding drops or disturbances in operating conditions can produce a random field around a drop, even when the applied macroscopic field is uniform.

Interscale energy transfers at the vicinity of the turbulent/nonturbulent interface are from small to large scales in directions close to the interface's tangent plane where motions are predominantly stretching, but from large to small scales in the other directions where motions are predominantly compressive and significantly correlated with square angular momentum. An important role in this predominance is played by the extreme compressive motions which can be significantly more likely than extreme stretching motions even where motions are on average stretching. The most intense interscale transfer rates and dissipation occur when the interface is as far as possible from the wake centerline.

The lifetime of a single bubble on the surface of an alcohol-water liquid bath is measured at intermediate humidity rates. Thanks to an automatic bubble generation device associated with a lifetime measuring device, we carry out a statistical study of the bubble lifetime, which extends over three decades, from 0.1 to 100 s. Up to alcohol concentrations of $12\%$ ($\mathrm{g}/\mathrm{g}$), the average bubble lifetime increases with the alcohol concentration. In addition, normalized lifetime probability density functions are independent of the alcohol concentration and relatively well described by a Weibull distribution with an exponent of $4/3$. We compare our experimental data with the predictions of a recent model highlighting the importance of Marangoni stresses induced by water contaminants to the fate of a bubble. In our case, these Marangoni stresses are probably induced by heterogeneities in the alcohol concentration maintained by evaporation.

Nature often uses capillary forces to manipulate fluids, which has inspired scientists to develop new applications, such as in microfluidics and laboratory-on-a-chip systems. Here we present a method to transport fluids in microfluidic channels, by exploiting the capillary interaction of fluid interfaces with traveling surface waves, called mechanowetting. We found that the three-phase lines of fluid slugs dynamically attach to the crests of the waves, resulting in fluid velocities that are equal to the wave speed. By comparing this microfluidic slug flow to conventional peristaltic fluid propulsion, we demonstrate that fluid velocities can be reached that are one order of magnitude larger. We quantified the efficiency numerically and theoretically in terms of the generated pressure gradient using a closed channel and measured the evolution of the pressure distribution as the wave progresses. The method was shown to work for a very wide range of contact angles. We anticipate that our results will lead to new microfluidic applications based on switchable topography technology.

Progress in the rapidly expanding exploration of planetary atmospheric and oceanic environments demands an adequate qualitative and quantitative representation of various processes in anisotropic turbulence. The existing analytical spectral theories are developed for homogeneous isotropic flows. They quickly become very complicated when expanded to anisotropic flows with waves. It is possible, however, to extend one such theory, the quasinormal scale elimination (QNSE), to stably stratified and rotating flows. Here the results of the theory are compared with a large variety of oceanic and atmospheric flows. These comparisons make it possible to clarify the physics of some processes governing the atmospheric and oceanic dynamics, quantify their spectra, and investigate their latitudinal and longitudinal variabilities. Some of the main results of this analysis are that vertical and horizontal spectra of atmospheric and oceanic turbulence can be derived within QNSE analytically; there exists a quantitative affinity between atmospheric and oceanic spectra; on large scales, spectral amplitudes are determined by the extra strains that cause flow anisotropization, rather than the energy or enstrophy fluxes; and planetary circulations appear to be amenable to classification as flows with compactified (compressed) dimensionality.

Liquid jets issued from a noncircular orifice exhibit oscillation owing to the surface tension. When the orifice has an $n$-fold rotational symmetry, a material cross section of the jet interchanges two symmetric shapes alternately. This oscillation, called axis switching, is a superposition of two ripples oppositely propagating in the azimuthal direction around the axis. In this study, we used computer simulations to demonstrate that we can pick up one of the two ripples by adjusting the initial velocity profile of the orifice. As a result of the single-wave propagation in the azimuth, the jet surface shows a twisted appearance. In contrast to the swirling jets, the twisted jet has no angular momentum around the axis. We numerically demonstrated the formation of twisted jets with various cross sections, including a regular square.

One class of active particles that is especially promising for biomedical microrobotic applications is rigid magnetic microswimmers propelled via rotation by a magnetic field. For these particles there is a maximum rotational frequency, hence velocity, determined by the maximum torque exerted by the field on the particle magnetization. It has been expected that velocity can always be increased by increasing the field magnitude to increase torque. This expectation holds if magnetization is constant or responds linearly to applied field, but all real materials actually respond nonlinearly, since as field strength increases the magnetization saturates and is coerced to point along the field direction. Here we show that this saturation and coercivity limit the maximum velocity of these microparticles. These effects are particularly important for soft magnetic materials. Although soft magnetic materials are used in many microswimmers, propulsion models incorporating their magnetic response are lacking. Our results are consistent with experimental observations and we predict that the limiting behavior occurs for common magnetic materials at typical rotational frequencies and field strengths, hence is relevant for current microswimmer design.

We show that the phase space of stratified turbulence mainly consists of two slow invariant manifolds with rich physics, embedded on a larger basin with fast evolution. A local invariant manifold in the vicinity of the fluid at equilibrium corresponds to waves, while a global invariant manifold corresponds to the onset of local convection. Using a reduced model derived from the Boussinesq equations, we propose that waves accumulate energy nonlinearly up to a point such that fluid elements escape from the local manifold and evolve fast to the global manifold, where kinetic energy can be more efficiently dissipated. After this, fluid elements return to the first manifold. As the stratification increases, the volume of the first manifold increases, and the second manifold becomes harder to access. This explains recent observations of enhanced intermittency and marginal instability in these flows. The reduced model also allows us to study structure formation, alignment of field gradients in the flow, and to identify balance relations that hold for each fluid element.

Many important applications in the food industry, biological systems, and recovery of fluids from the subsurface involve multiphase flow dynamics where one of the phases is a non-Newtonian, viscoelastic fluid. In this work, we investigate the role of viscoelastic displacing fluids in recovering trapped nonwetting fluids. We perform the lattice Boltzmann (LB) modeling of wetting viscoelastic fluids described by a Maxwell model that displace nonwetting, trapped droplets in three different pore geometries. Results show the oscillation of the trapped nonwetting droplets and subsequent release induced by the viscoelasticity of the displacing fluid. The oscillation behaviors are in qualitative agreement with recent experiments in microfluidic chips and micromodels. The disorder of streamlines in viscoelastic fluids is reported in the presence of another phase, which explains the observation of oscillations. In the geometry of a capillary tube that converges to a smaller constriction/throat, a vortex downstream of the droplet is found to prevent the droplet from entering the throat. In the geometry of a tube with an “x-shaped” solid grain, we find that the oscillation strength and extraction capability of displacing fluids monotonically increases with their elasticity. The results from the geometry of a tube with a “dead-end” branch show a linear relationship between the average mean vorticity and the square root of the Deborah number before the release of droplets.

Characteristics of near-wall turbulence at quasistationarity under strong wall cooling are studied using direct numerical simulation of open-channel flow. It is shown that if turbulence reaches quasistationarity, then the characteristics of quasistationary near-wall turbulence, even with the strongest wall cooling rate, are generally similar to the weakly stratified case. The effects of strong stable stratification on the characteristics of near-wall turbulence are transient. The effect of stratification on several characteristics of stratified near-wall turbulence, including first-, second-, and higher-order statistics, turbulent kinetic energy budget, and mechanisms involved in the evolution of turbulence producing eddies, are discussed. It is shown that among mechanisms that contribute to the budget of turbulent kinetic energy, transfer and pressure-work are more dependent on the stratification if turbulence reaches quasistationarity. The buoyancy destruction term influences the budget for the tangential Reynolds stress more than the budget for the turbulent kinetic energy. Relevant length scales are also discussed in detail. The Corrsin and Ellison scales are smaller than the Ozmidov scales and are sensitive to stratification in the upper logarithmic layer and in the outer layer. The Corrsin scales in the lower half of the buffer layer and fine-scale structures of wall-normal velocity in the viscous sublayer are smaller than the Kolmogorov scale. Finally, the effect of heat entrainment from the upper boundary and computational domain size are also examined. In summary, it is found that the behavior of near-wall turbulence at quasistationarity is approximately similar to weakly stratified cases, regardless of the choice of upper boundary condition.

A series of laboratory experiments on energy-conserving gravity currents in a lock-exchange facility are conducted for a range of Reynolds numbers, $\text{Re}=\frac{U_{F}h}{\nu }=485–12270$, where $U_F$ is the front velocity of the current, $h$ the current depth, and $\nu$ the kinematic viscosity of the fluid. The velocity and density fields are captured simultaneously using a particle image velocimetry–planar laser induced fluorescence system. A moving average method is employed to compute the mean field and a host of turbulence statistics, namely, turbulent kinetic energy ($K$), shear production ($P$), buoyancy flux ($B$), and energy dissipation ($\epsilon$) during the slumping phase of the current. The subsequent findings are used to ascertain the quantitative values of mixing efficiency, ${\text{Ri}}_f$, Ozmidov length scale ($L_o$), Kolmogorov length scale ($L_{\kappa }$), and eddy diffusivities of momentum (${\kappa }_m$) and scalar (${\kappa }_{\rho }$). Two different forms of ${\text{Ri}}_f$ are characterized in this study, denoted by ${\text{Ri}}_f^I=\frac{B}{P}$ and ${\text{Ri}}_f^{II}=\frac{B}{B+\epsilon }$. The results cover the entire diffusive regime (3 $<{\text{Re}}_b<$ 10) and a portion of the intermediate regime (10 $<{\text{Re}}_b<$ 50), where ${\text{Re}}_b=\frac{\epsilon }{\nu N^2}$ is the buoyancy Reynolds number that measures the level of turbulence in a shear-stratified flow, with $N$ being the Brunt-Väisälä frequency. The variation of turbulence quantities, $\overline{P}\left(z\right)$, $\overline{B}\left(z\right)$, and $\overline{\epsilon }\left(z\right)$, along the depth of the current shows a marked increase at the interface of the ambient and current fluids, owing to the development of a shear-driven mixed layer. Based on the changes in the turbulence statistics and the length scales, it is inferred that the turbulence decays along the length of the current. The mixing efficiency monotonically increases in the diffusive regime (${\text{Re}}_b<10$) and is found to be $\overline{{\text{Ri}}_f^I}\approx$ 0.15 and $\overline{{\text{Ri}}_f^{II}}\approx$ 0.2 in the intermediate regime. Using the value of $\overline{{\text{Ri}}_f^{II}}$, the normalized eddy diffusivity of momentum is parameterized as $\frac{{\kappa }_m}{\nu .{\text{Ri}}_g}=1.2{\text{Re}}_b$, where ${\text{Ri}}_g$ is the gradient Richardson number, and the normalized eddy diffusivity of scalar is parameterized as $\frac{{\kappa }_{\rho }}{\nu }=0.2{\text{Re}}_b$.

In this study, the dynamic one-equation-based subgrid model for large-eddy simulation (LES) of turbulent flows is extended to account for the effects of density stratification under the Boussinesq approximation. The model utilizes an eddy viscosity closure by solving a modeled transport equation for the subgrid-scale (SGS) turbulent kinetic energy ($k^{\mathrm{sgs}}$) to obtain the characteristic velocity scale. The closure of the SGS density flux is attained through an algebraic eddy diffusivity-based approach using the eddy viscosity and the turbulent Prandtl number. The transport equation for $k^{\mathrm{sgs}}$ gets modified due to density stratification, which leads to a coupling of the SGS stress and the SGS density flux. All the model coefficients are determined locally in a dynamic manner. The dynamic model is evaluated by simulating a fully developed turbulent flow in a periodic channel under neutral and stratified conditions at frictional Reynolds number (${\mathrm{Re}}_{\tau }$) of 180, 550, and 950 and frictional Richardson number (${\text{Ri}}_{\tau }$) of 0, 60, 120, and 240. The LES predictions are compared with direct numerical simulation results. A comprehensive assessment is performed by examining the behavior of the model coefficients, comparison of static and dynamic approaches for the model coefficients, along with comparison with other well-established algebraic closures for the SGS stress and the SGS density flux at ${\text{Re}}_{\tau }=550$. The results show that the proposed model appropriately responds to the changes in the behavior of the flow due to stratification, at both the resolved and the SGS levels, particularly in the regions away from the wall where internal waves tend to coexist with the shear-generated turbulence. An explicit coupling of the SGS buoyancy flux with the SGS kinetic energy in the dynamic model, which is absent in the other algebraic models, allows improved accuracy in capturing the instantaneous and the statistical features of both the resolved and the SGS quantities.

Strictly axisymmetric turbulence, i.e., turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two- and three-dimensional turbulence. We investigate statistically steady states of this system by direct numerical simulation using a forcing protocol, which allows the injected energy in the toroidal and in the poloidal directions to be tuned independently. A sharp transition between a two-dimensional two-component (2D2C, non-swirling) flow and a two-dimensional three-component (2D3C, swirling) flow is observed. We derive a statistical model which reproduces this transition.

We generate and observe large (∼1 m diameter) anticyclonic vortices in a stably stratified rotating tank that are neutrally buoyant. A nonaxisymmetric ($m=2$) instability quickly develops, leading to subvortices and fine-structured shed filaments. When heated with respect to their surroundings the vortex lenses behave much the same way but with two conspicuous additions. First, prominent early, is that the circumferential edge appears serrated with cusplike features from lateral intrusions, surmised to be due to thermal convection. Second, a stepped upper layer develops due to thermohaline diffusive convection. We see no evidence of layering in the nonheated cases, indicating that viscohaline double diffusion appears to be inoperative, likely prevented by a turbulent background. These observations are considered with respect to previous laboratory work as well as to geophysical vortices that are thermally distinct from their environs, such as Meddies.

A general formulation is presented for studying the motion of buoyant vortices in a homogeneous ambient fluid. It extends the well-known Hamiltonian framework for interacting homogeneous point vortices to include buoyancy effects acting on the vortices. This is then used to systematically examine the buoyant one-, two-, and three-vortex problems. In doing so we find that two buoyant vortices may evolve either as a pair in bounded circular orbits or as two independent unbounded vortices that drift apart, and a criterion is found to distinguish these cases. Special attention is given to the buoyant vortex couple, consisting of two vortices of equal and opposite circulation and equal buoyancy anomaly. We show that a theoretical maximum height is generally possible for the rise (or fall) of such couples against buoyancy forces. Finally, the possibility and onset of chaotic motions in the buoyant three-vortex problem are addressed. In contrast to the homogeneous three-vortex problem, the buoyant vortex system shows evidence that chaos is present. We also demonstrate the chaotic advection of tracer parcels arising from the flow field induced by just two buoyant vortices.

Geophysical fluid flows are predominantly turbulent and often strongly affected by the Earth's rotation, as well as by stable density stratification. Using direct numerical simulations of forced Boussinesq equations, we study the influence of these effects on the motion of fluid particles. We perform a detailed study of Lagrangian statistics of acceleration, velocity, and related quantities, focusing on cases where the frequencies associated with rotation and stratification (RaS), $f$ and $N$, respectively, are held at a fixed ratio $N/f=5$. The simulations are performed in a periodic domain, at Reynolds number $\text{Re}\approx 4000$, and Froude number Fr in the range $0.03\lesssim \text{Fr}\lesssim 0.2$ (with Rossby number $\text{Ro}=5\text{Fr}$). As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which corresponds to $\text{Fr}\lesssim 0.07$. For the given runs, this transition to a wave-dominated regime can also be seemingly described by simply comparing the timescales $1/N$ and ${\tau }_{\eta }$, the latter being the Kolmogorov timescale based on the mean kinetic energy dissipation. Due to the known anisotropy induced by RaS, we consider separately the motion in the horizontal and vertical directions. In the regime $N{\tau }_{\eta }<1$, acceleration statistics exhibit well known characteristics of isotropic turbulence in both directions, such as probability density functions with wide tails and acceleration variance approximately scaling as per Kolmogorov's theory. In contrast for $N{\tau }_{\eta }>1$, they behave very differently, experiencing the direct influence of the imposed rotation and stratification. On the other hand, the Lagrangian velocity statistics exhibit visible anisotropy for all runs; nevertheless the degree of anisotropy becomes very strong in the regime $N{\tau }_{\eta }>1$. We observe that in the regime $N{\tau }_{\eta }<1$, rotation enhances the mean-square displacements in horizontal planes in the ballistic regime at short times but suppresses them in the diffusive regime at longer times. This suppression of the horizontal displacements becomes stronger in the regime $N{\tau }_{\eta }>1$, with no clear diffusive behavior. In contrast, the displacements in the vertical direction are always reduced. This inhibition is extremely strong in the $N{\tau }_{\eta }>1$ regime, leading to a scenario where particles almost appear to be trapped in horizontal planes.