We studied homogeneous stably stratified turbulence in a triply periodic domain over a wide range of stratification strengths. We evaluated the statistically stationary, volume-averaged budgets of Reynolds stresses, turbulent potential energy, and turbulent vertical density flux. By separately studying the three components of the turbulent kinetic energy (TKE), we examined the role of pressure-strain correlations and observed connections between changes in the energetics to regime shifts of the mixing coefficient $\left(\mathrm{\Gamma }\right)$ as a function of the turbulent Froude number $\left({\text{Fr}}_k\right)$. As we increase stratification, we find that pressure-strain correlations become more important in producing the vertical component of TKE $\left(k_w\right)$. At the stratification strength where direct production and pressure-strain correlations equally generate $k_w$, we observe the maximum value of $\mathrm{\Gamma }$, and it remains constant as stratification is increased further. However, when we greatly increase stratification from this point, the pressure-strain correlations become the dominant source of $k_w$ with direct production becoming negligible, and this change is accompanied by the mixing coefficient decreasing from its maximum value. Finally, we find that this final transition for the mixing coefficient coincides with a sign change of the pressure scrambling term in the vertical density flux budget.

The evolution of the liquid bridge formed between two coalescing sessile yield-stress drops is studied experimentally. Surprisingly, we find that the height of the bridge evolves similar to a Newtonian fluid as $h_0\left(t\right)\sim t$, before arresting at long time due the fluid's yield stress. From viscoplastic lubrication theory we find a model for the arrested interface shape based on the balance between capillary pressure and yield stress. We then solve numerically for this final arrested profile shape and find it to depend on the fluid's yield stress ${\tau }_y$, the surface tension coefficient $\sigma$ and the coalescence angle $\alpha$, represented by a modified Bingham number. We also present a scaling argument for the bridge's temporal evolution using the length scale found from this arrested shape analysis and present a similarity solution for the spatial evolution of the liquid bridge.

This paper presents a methodology to calculate the sensitivity of the least stable eigenvalues with respect to an external forcing added in a fluid-structure interaction system. The structure is a rigid circular cylinder. The algorithms were implemented using the spectral/$hp$ element method for the spatial discretization. We make use of the adjoint equations of the flow-structure coupled system to provide the regions more receptivity to an external forcing. Next, sensitivity computations are carried out by setting the external forcing proportional to the flow velocity and applied in a local point in the domain. The fields of sensitivity were analyzed by using the two least stable modes for different values of reduced velocity. The results were compared to those obtained for a fixed cylinder at the same Reynolds number. Our main findings reveal that the sensitivity fields of the fluid-structure interaction system can be very different from its fixed structure counterpart, and among the cases, with an elastic structure, the fields vary according to the reduced velocity. The sensitivity results were verified against linear and nonlinear simulations of flows with small control cylinders placed at locations selected according to the sensitivity fields. The agreement between the predictions made with the sensitivity analyses and the linear and nonlinear results of the forced flows was excellent. Furthermore, evaluating the sensitivity predictions based on the two least stable modes can be essential if the goal is attenuate the vortex-induced vibration.

Microswimmer suspensions self-organize into complex spatiotemporal flow patterns, including vortex lattices and mesoscale turbulence. Here we explore the consequences for the motion of passive tracers, based on a continuum model for the microswimmer velocity field. We observe two qualitatively different regimes distinguished via the dimensionless Kubo number $K$. At advection strengths right above the transition to turbulence, the flow field evolves very slowly ($K\gg 1$) and the spatial vortex structures lead to dominant trapping effects. In contrast, deep in the turbulent state, much faster dynamics ($K\ll 1$) consistent with the so-called sweeping hypothesis leads to transport properties completely determined by the temporal correlations. In between ($K\approx 1$), we observe a regime of optimal transport, signaled by a maximum of the diffusion coefficient.

The investigation of the fall of a sphere at finite Reynolds number in a concentrated suspension of small fluidized particles leads to unexpected results. By analyzing the drag force, it is shown that the average surface stress on the sphere is independent of the size of the sphere. It is proportional to an effective viscosity determined from the sedimentation velocity of the particles multiplied by the velocity of the sphere and divided by the size of the particles. These results question the role of concentration inhomogeneities that occur on a large scale in the overall flow around a moving obstacle and on a small scale near its surface.

The force partitioning method [Menon and Mittal, J. Fluid Mech. 918, R3 (2021)] is employed to decompose and analyze the pressure-induced drag for turbulent flow over rough walls. The pressure drag force imposed by the rotation-dominated vortical regions ($Q>0$, where $Q$ is the second invariant of the velocity gradient tensor) and strain-dominated regions ($Q<0$) are quantified using a geometry dependent auxiliary potential field (denoted by $\varphi$). The analysis is performed on data from direct numerical simulations (DNSs) of turbulent channel flows, at frictional Reynolds number of ${\text{Re}}_{\tau }=500$, with cube and sand-grain roughened bottom walls. Results from both simulations indicate that the $Q$-induced pressure drag is the largest contributor (more than 50%) to the total drag on the rough walls. Data are further analyzed to quantify the effects of time-mean (coherent) and incoherent turbulent flow on the $Q$-induced drag force, and to discuss possible effects of roller and U-shaped structures expected to occur at the crest and midcrest locations of the roughness elements, respectively. Based on the observation that the $\varphi$ field encodes information about the surface geometry that directly impacts the drag, we provide initial evidence that it can also be used to parametrize the surface drag. Specifically, we propose and test three norms based on the $\varphi$ field (two of them related to the surface-induced potential flow), and explore the characterization of the Nikuradse equivalent sand-grain height $k_s$ based on these parameters for a number of channel flows with different roughness topologies. Data are provided from a suite of DNS cases by Aghaei-Jouybari et al. [J. Fluid Mech. 912, A8 (2021)]. An empirical correlation depending on these $\varphi$-based parameters, with five empirically tuned coefficients, is shown to predict $k_s$ with average and maximum errors of 10.5 and 26 percent, respectively. The results confirm that a purely geometric quantity, the $\varphi$ field, provides useful additional information that can be used in drag law formulations.

Objects inserted in a fast-flowing soap film are observed to cause strong disturbances on the film, resembling shock waves. Currently a prevailing opinion is that these shock waves correspond to sudden increases in film thickness caused by elastic symmetric waves, or the propagation of film thickness changes driven by surface tension variations with the film surface area. Here, we show by laser interferometry that these “shock waves” in fact originate from the antisymmetric waves studied by Taylor, which correspond to the bending of the liquid film with no thickness change. This phenomenon thus forms an example of symmetry breaking. These shock waves maintain an antisymmetric structure, but the structure size varies with the size of the intruding object. Our results indicate that these structures could be objects for studying solitary waves, rather than the traditional shocks corresponding to density jumps in compressible flows.

Analyzing and sorting particles and/or biological cells in microfluidic devices is a topical problem in soft-matter and biomedical physics. An easy and rapid screening of the deformation of individual cells in constricted microfluidic channels allows, for example, the identification of sick or aberrant cells with altered mechanical properties, even in vast cell ensembles. The subsequently desired softness-specific segregation of cells is, however, still a major challenge. Moreover, aiming at an intrinsic and unsupervised approach raises a very general question: How can one achieve a softness-dependent net migration of particles in a microfluidic channel? Here, we show in a proof-of-principle experiment that this is possible by exploiting a deformation-induced actuation of soft cells in asymmetric periodic flow fields in which rigid beads show a vanishing net drift.

The use of streamwise grooves for intensification of streaks created by heating in shear layers has been investigated. Three ranges of groove wave numbers were of interest: wave numbers near the critical wave number of the Rayleigh-Bénard (RB) instability, wave numbers characterizing drag-reducing grooves, and the optimal wave numbers. It is shown that uniform heating of a grooved surface produces intense streaks only when the groove wave number is near the critical RB wave number and the heating intensity exceeds the critical RB intensity. The use of long-wavelength grooves reduces flow losses, but the resulting streaks are less intense. The use of heating patterns tuned with groove patterns can produce very intense streaks whose spatial distribution is easily controlled through selection of the patterns’ wave number. An increase of flow losses due to patterned heating can be compensated for using spatial groove distributions with drag-reducing capabilities. It has been demonstrated that the most effective wave number producing high-intensity streaks at low flow losses is between the RB wave number and the drag-reducing wave numbers—this optimal wave number has been identified.

The unchannelized collapse of wet granular columns in the pendular state is investigated experimentally. Three different collapse regimes are observed in experiments, which are significantly dependent on the particle size as well as the initial aspect ratio of the column, while the water content has a quantitative effect on final deposit morphology. A dimensionless number containing the particle size and the water content is proposed to quantitatively characterize the macroscopic cohesion induced by the presence of water. On this basis, a phase diagram is put forward for describing different collapse regimes of wet granular materials. Furthermore, the dynamics and the resulting deposit morphology after collapse are primarily examined based on a series of experiments, particularly in two typical collapse regimes, where the coupling effects of particle size, water content, and initial aspect ratio of the column are mainly considered. Finally, generalized scaling laws have been developed to characterize the dependency of the deposit morphology on two relevant variables: the initial aspect ratio and the proposed dimensionless parameter. The morphological quantities in the wet case may be determined by respectively adding the variations caused by the cohesion effect to the results of dry granular material. The proposed scaling laws can be well degraded to those obtained in dry granular material when the cohesive effect inside wet granular material is weak enough. This implies that generalized scaling laws can be applicable to the collapse of granular material in a wider range of situations.

Despite the well-known limitations of linear stability theory in describing nonlinear and turbulent flows, it has been found to accurately capture the transitions between certain nonlinear flow behavior. Specifically, the transition in heat flux scaling in rotating convective flows can be well predicted by applying a linear stability analysis to simple profiles of a convective boundary layer. This fact motivates the present study of the linear mechanisms involved in the stability properties of simple convective setups subject to rotation. We look at an idealized two-layer setup and gradually add complexity by including rotation, a bounded domain, and viscosity. The two-layer setup has the advantage of allowing for the use of wave interaction theory, traditionally applied to understand stratified and homogeneous shear flow instabilities, in order to quantify the various physical mechanisms leading to the growth of convective instabilities. We quantitatively show that the physical mechanisms involved in the stabilization of convection by rotation take two different forms acting within the stratified interfacial region, and in the homogeneous mixed layers. The latter of these we associate with the tendency of a rotating flow to develop Taylor columns (TCs). This TC mechanism can lead to both a stabilization or destabilization of the instability and varies depending on the parameters of the problem. A simple criterion is found for classifying the influence of these physical mechanisms.

We present numerical simulations of turbidity currents generated by a moving source that model particle clouds released by underwater vehicles such as those used in deep-sea dredging and mining. We use two approaches to model the flow and resulting deposits. First, we adapt the shallow-water equations to include a moving source of both momentum and particles. Second, we modify the classical box model to include a moving source. We validate our simulations before studying the impact of the most important governing dimensionless parameters: a vehicle Froude number Fr based on the depth of sediments being resuspended and the dimensionless settling speed of those sediments, $u_s$. We find that Fr is most determinant in the current and deposit shape, with $\text{Fr}>2$ resulting in elongated shapes and $\text{Fr}<2$ resulting in rounder ones, and that $u_s$ determines the rate at which deposits grow. Another parameter, the vehicle's drag coefficient, was found not to have much effect beyond the immediate vicinity of the vehicle. Overall, both models found similar trends. The box model, much less computationally expensive, was less accurate when spatial nonuniformities developed, as happens at long times, but captured the early spreading rate well. The shallow-water equations handled nonuniformities correctly but tended to over-predict the spreading rate. We used the insight gained from those simulations to obtain criteria for the maximum extent of deposits left but such currents in both the low and high Froude number regimes.

The response of a turbulent separation bubble (TSB) to zero-net-mass-flux actuation is investigated via direct numerical simulations. Rectangular jets with their long axis oriented in the streamwise direction are used to generate unsteady streamwise vortices that mimic the streamwise elongated Görtler vortices found to be associated with the low-frequency unsteadiness of the TSB [Wu et al., J. Fluid Mech., 883, A45 (2019)]. Three sinusoidal actuation frequencies are investigated, corresponding to the two natural frequencies of the undisturbed separation bubble ($f_l$ and $f_h$ with a ratio of $f_h/f_l=2.5$) and a high frequency at $10f_l$ motivated by a harmonic resolvent analysis. The results are compared to the baseline uncontrolled flow. Very-large scale (VLS), spanwise-rotating vortices are formed at $f_l$ and $f_h$, causing a 50% reduction in the mean TSB length. A counter-rotating secondary vortex is induced locally by the VLS vortex in the $f_l$ case and forms a vortex pair with the VLS vortex as they move downstream together. The interaction of the vortex pair facilitates their decay. The VLS vortex generated by the forcing at $f_h$ is not strong enough to produce such a secondary vortex. Spectral analysis of the harmonic resolvent operator is used to quantify the receptivity of the flow to actuation at different frequencies. The perturbations that excite the most energetic response in the flow are indeed in the form of streamwise-elongated structures in the separation region at $f_l$ and $f_h$. Energetic structures corresponding to the temporal mean obtained from the analysis are found to extend to distances far downstream of the separation bubble confirming the great sensitivity of the entire flow to such forcing.

Large eddy simulations are performed to study tonal noise generation by a NACA0012 airfoil at an angle of attack $\alpha =3$ deg. and freestream Mach number of $M_{\infty }=0.3$. Different Reynolds numbers are analyzed spanning $0.5\times {10}^5\le \mathrm{Re}\le 4\times {10}^5$. Results show that the flow patterns responsible for noise generation appear from different laminar separation bubbles, including one observed over the airfoil suction side and another near the trailing edge, on the pressure side. For lower Reynolds numbers, intermittent vortex dynamics on the suction side results in either coherent structures or turbulent packets advected towards the trailing edge. Such flow dynamics also affects the separation bubbles on the pressure side, which become intermittent. Despite the irregular occurrence of laminar-turbulent transition, the noise spectrum depicts a main tone with multiple equidistant secondary tones. Increasing the Reynolds number leads to a permanent turbulent regime on the suction side that reduces the coherence level causing only small scale turbulent eddies to be observed. Furthermore, the laminar separation bubble on the suction side almost vanishes while that on the pressure side becomes more pronounced and permanent. As a consequence, the dominant noise generation mechanism becomes the vortex shedding along the wake.

We report frictional drag reduction and a complete flow relaminarization of elastic turbulence (ET) at vanishing inertia in a viscoelastic channel flow past an obstacle. We show that the intensity of the observed elastic waves and wall-normal vorticity correlate well with the measured drag above the onset of ET. Moreover, we find that the elastic wave frequency grows with the Weissenberg number, and at sufficiently high frequency it causes a decay of the elastic waves, resulting in ET attenuation and drag reduction. Thus, this allows us to substantiate a physical mechanism, involving the interaction of elastic waves with wall-normal vorticity fluctuations, leading to the drag reduction and relaminarization phenomena at low Reynolds number.

This study investigates the acoustic streaming phenomena in a standing surface acoustic wave driven microfluidic channel filled with second-order fluids. We have developed a multiple-timescale-based theoretical model where a perturbation technique was adopted to separate the fast and slow timescales associated with the oscillatory flow field (i.e., acoustic field) and the mean flow field (acoustic streaming), respectively. The governing equations have been expressed in nondimensional form to effectively show the dependence of the acoustic streaming fields on Reynolds number (Re), Deborah number (De), and the ratio of material constants related to normal stress coefficients $\left(b\right)$. Contrary to our intuition, we observed that with increasing Deborah number (which is a measure of the extra stress present in the second-order fluids), acoustic streaming first increases and thereafter, a further increase in Deborah number leads to a gradual suppression of streaming. Our study also reveals that the acoustic field and the acoustic radiation force show negligible dependence on the fluid rheology. For the following ranges, $0.08\le \mathrm{Re}\le 0.32$, $0\le \mathrm{De}\le 1$, and $0\le b\le 100$, the maximum variation of the acoustic streaming is observed to be $\sim 161.3\%$, whereas the variation in the acoustic field stays within just 0.15%. This significant finding can help design efficient acoustofluidic systems that can manipulate acoustic streaming without affecting the acoustic radiation forces, as strong acoustic streaming can impair the acoustofluidic devices.

The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial economic savings in energy and input ingredients. Enhancements in mixing efficiency can be accomplished by unorthodox stirring protocols as well as modified stirrer shapes that utilize unsteady hydrodynamics and vortex-shedding features to instigate the formation of fluid filaments which ultimately succumb to diffusion and produce a homogeneous mixture. We propose a PDE-constrained optimization approach to address the problem of mixing enhancement for binary fluids. Within a gradient-based framework, we target the stirring strategy as well as the cross-sectional shape of the stirrers to achieve improved mixedness over a given time horizon and within a prescribed energy budget. The optimization produces a significant enhancement in homogeneity in the initially separated fluids, suggesting promising modifications to traditional stirring protocols.

We report results from an experimental investigation on the fluid-structure interactions of flapping foils with tapered thickness profiles actuated in a quiescent viscous fluid. We seek to assess the propulsive performance of two sets of flapping foils; one with a fixed average bending stiffness, the other one with a fixed mass ratio. We find that foils that are stiffer towards the root than at their tip produce higher values of thrust and efficiency simultaneously, over a wide range of driving frequencies. Our kinematic analysis reveals that more tapered foils naturally develop a traveling-wave-dominated motion. We perform particle image velocimetry to relate the dynamics and kinematics of the flapping foils to the dynamics of the surrounding fluid. For more tapered foils, we observe a stronger vorticity production and a wake pattern with enhanced downstream speed of the fluid. Our paper provides experimental evidence that tapered stiffness distributions robustly enhances propulsive performance.

We study the long-time behavior of an advection-diffusion equation with a general time-varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar field at long times by using the center manifold theory. We carefully compare it with existing time-varying homogenization theory as well as other existing center manifold based studies and present conditions on the flows under which our new approximations give a substantial improvement to these existing theories. A recent study [Ding et al., Physica D 432, 133118 (2022)] has shown that Gaussian random shear flows induce a deterministic effective diffusivity at long times and explicitly calculated the invariant measure. Here, with our established asymptotic expansions, we not only concisely demonstrate those prior conclusions for Gaussian random shear flows but also generalize the conclusions regarding determinism to a much broader class of random (non-Gaussian) shear flows. Such ergodicity-like results are important since they assure an experimentalist only need to perform a single realization of a random flow to observe the ensemble moment predictions at long times. Monte Carlo simulations are presented illustrating how the highly random behavior converges to the deterministic limit at long times. Counterintuitively, we present a case demonstrating that the random flow may not induce larger dispersion than its deterministic counterpart and in turn present rigorous conditions under which a random renewing flow induces a stronger effective diffusivity. Last, for white in time flows and renewing flows, we derive the invariant measure and explore its Peclet number dependencies.

We conducted laboratory experiments to quantify the effect of low concentrations of clay, $C\in [0,2]\%$, on turbulence in water-clay flows under nearly isotropic conditions using a novel approach. Full optical access was possible using Laponite RD™, a synthetic clay capable of producing clear suspensions of clay particles. Turbulence was generated in a customized cubic mixing box using flow actuators placed symmetrically at each of the eight corners. High-frame-rate particle image velocimetry was used to quantify the spatiotemporal dynamics of turbulence around the center of the mixing box. The results showed that the presence of clay particles strongly modulated the structure of turbulence. Monotonic reduction of the turbulent kinetic energy (TKE) and mean dissipation rate $\langle \epsilon \rangle$ and increase of the Taylor microscale $\lambda$ was induced by increasing the clay concentration. In particular, the measurements indicated a relation between clay concentration and the $p$ factor, the known Kolmogorov power-law correction $-5/3+p\left({\text{Re}}_{\lambda }\right)$ of the inertial subrange, where ${\text{Re}}_{\lambda }$ is the Taylor microscale Reynolds number. The $p$ factor decreased approximately linearly within $1\%\lesssim C\lesssim 2\%$. This parameter and the third-order structure function $S_3$ supported the scale changes obtained from direct estimation with particle image velocimetry (PIV) data. These results demonstrated the significant impact of clay on the multiscale dynamics of turbulence even at low clay concentrations.