Faraday waves are created in experiment by mechanically vibrating a cylindrical container. Frequency scans are performed, and the acceleration threshold above which a surface wave appears is measured using a laser light approach, giving the instability tongue in frequency-acceleration space. The spatial structure of the surface wave, which conforms to the cylindrical container for wavelengths comparable to the container size, is determined using long-exposure-time white light imaging and is defined by the mode number pair $(n,\ell )$. Edge conditions at the container sidewall are controlled to create a (i) pinned or (ii) freely sliding contact-line. The driving frequency with the smallest threshold acceleration is identified as the natural frequency for that particular mode number pair. A theoretical model is developed using a viscous potential approximation to compute the natural oscillations of a viscoelastic material in a cylindrical container with a flat interface for both a pinned and a freely sliding contact-line. A closed-form expression is given for the freely sliding case, and a Rayleigh-Ritz procedure is used for the pinned case. The agreement is good between theoretical predictions and experimental observations for Triton/water mixtures, glycerol/water mixtures, and agarose gels, notwithstanding the large range in parameter space and the very different boundary conditions considered.

Granular beds driven by overlying shear flows begin to erode when the stress delivered to the bed by the fluid exceeds a critical value. Previous studies have shown that this critical stress depends on the stress history of the bed, and that beds will strengthen when subjected to subcritical stresses. By measuring the behavior of erodible beds in a laboratory flume, we confirm this strengthening effect, but also find that it is strongly directional. We find that preconditioned granular beds are indeed more resistant to erosion when driven in the direction of the conditioning flow, but that this strengthening is accompanied by a weakening when driven in other directions. Preconditioned beds are in fact more susceptible to erosion by flows in the direction opposite to that of the conditioning flow than freshly settled beds are. Our results show that the strength of a natural erodible bed with a stress history is likely to be highly anisotropic, with significant implications for predictions of sediment transport.

To date, the Leidenfrost effect has been a two-phase phenomenon: either an evaporating liquid or a sublimating solid levitates on its vapor. Here, we demonstrate that an ice disk placed on a sufficiently hot surface exhibits a three-phase Leidenfrost effect, where both liquid and vapor films emanate from under the levitating ice. Curiously, the critical Leidenfrost temperature was about 400 ${}^{\circ }\mathrm{C}$ hotter for ice than for a water drop. As a result, the effective heat flux was an order of magnitude larger when quenching aluminum with ice rather than water over a wide temperature range of 150–550 ${}^{\circ }\mathrm{C}$. An analytical model reveals the mechanism for the delayed film boiling: the majority of the surface's heat is conducted across the levitating meltwater film due to its 100 ${}^{\circ }\mathrm{C}$ temperature differential, leaving little heat for evaporation.

In turbulent bluff body flows, the presence of vortex shedding, a form of coherent structures (CS), introduces a new characteristic scale that is distinct from the scale of background stochastic turbulence (ST). This double-scale picture essentially invalidates the conventional single-scale modeling for the turbulence energy dissipation in steady Reynolds-averaged-Navier-Stokes (RANS) simulations. In this paper, we present a conceptual model to quantify the uncertainty in the steady-RANS dissipation closure for flows past bluff bodies with vortex shedding. This model is developed in two steps. First, we formulate a double-scale, double-linear-eddy-viscosity (DSDL) framework for the transport of CS and ST energy, with an undetermined energy transfer rate from CS to ST. In this framework, the dissipation of ST energy follows a conventional transport model; the length scale of CS is determined such that the CS energy is intensely produced in free shear layers. Second, we design a functional form for the energy transfer rate based on a qualitative analysis and an analogy with the “return-to-isotropy” process. This form contains two uncertain parameters that control the CS-ST interaction. Subsequently, the DSDL model is tested on simulations of the flows past circular and square cylinders, and of the flow in a pin-fin array. In all cases, the model provides a significant improvement upon both conventional models and models with Reynolds stress shape perturbations. The sizes of the recirculation zones are accurately predicted, and simulations with varying values for the uncertain parameters predict intervals for the peak turbulence kinetic energy that encompass reference data.

In climate predictions, clouds are the leading source of uncertainty. This is partly because, to simulate the fluid dynamics of climate over the entire globe, a large grid spacing must be used, so clouds are a subgrid-scale parametrization rather than a resolved feature. Here, a framework is investigated with finer grid spacing of $O\left(1\right)$ or $O\left(10\right)\mathrm{km}$ so that some clouds are not subgrid-scale; instead, clouds evolve on the numerical grid. This cloud evolution is achieved using stochastic modeling. Hence, the framework is idealized in the sense that the full fluid dynamics of cloud circulations is still not resolved, and simplified vertical structures are used. Nevertheless, the fluid dynamics model includes evolving clouds that interactively adjust in size, shape, lifetime, and regional coverage. In addition, different cloud types are included with different roles in the climate system, including deep convective clouds and also boundary-layer clouds such as shallow cumulus and stratocumulus clouds. Other basic aspects of the idealized climate system are planetary-scale circulations (e.g., Walker circulation) and radiation. With these ingredients (evolving clouds, planetary-scale circulations, and radiation), the framework has the potential for idealized investigations of climate change with interactive cloud–radiative feedback of individual clouds. Here, the formulation of the model equations is presented, and numerical simulations are shown to illustrate the model dynamics and climate change.

We numerically investigate flow regimes of rotating Rayleigh-Bénard convection on a horizontally periodic domain vertically bounded by no-slip walls from a statistical viewpoint. The flow is subject to strong thermal forcing [Rayleigh number up to $\text{Ra}=\mathit{O}\left({10}^{12}\right)$] and rapid rotation [Ekman number down to $\text{Ek}=\mathit{O}\left({10}^{-7}\right)$]. Various Prandtl numbers ($\text{Pr}=0.1, \approx 5$, and 100) are considered. In the explored parameter space, we observe the regimes of quasisteady cells, convective Taylor columns, plumes, large-scale vortices (LSVs), and rotation-affected convection. Time- and horizontally averaged statistics such as mean temperature, root-mean-square (RMS) temperature, and RMS velocity are used to discuss the thermal mixing and convective heat transfer (Nusselt number $\text{Nu}$) in each regime. For cells and columns, both the mean temperature gradient at midheight ($-{\partial }_z{\langle T\rangle |}_{z=0.5}$) and $\text{Nu}$ exhibit scalings with flow supercriticality that are consistent with predictions from numerical models of asymptotically rapidly rotating convection. For LSVs at moderate supercriticality, $-{\partial }_z{\langle T\rangle |}_{z=0.5}$ saturates, akin to what is observed in geostrophic turbulence in asymptotic studies. Interestingly, for LSVs at larger supercriticality, $-{\partial }_z{\langle T\rangle |}_{z=0.5}$ decreases, a behavior that is instead in line with the recently experimentally observed regime of so-called rotationally influenced turbulence. We also explore flow statistics near the top and bottom walls. The statistical distribution of temperature at the edge of the kinetic boundary layer (BL) depends on the relative thickness of this layer (${\delta }_u$) and the thermal BL (${\delta }_{\theta }$). In cases where ${\delta }_u>{\delta }_{\theta }$, the temperature distribution at $z={\delta }_u$ is positively skewed, suggesting coherent localization of hot rising fluid; the distribution is negatively skewed at $z=1-{\delta }_u$, denoting localized cold sinking fluid. In contrast, when ${\delta }_u<{\delta }_{\theta }$, hot fluid at $z={\delta }_u$ (cold fluid at $z=1-{\delta }_u$) occupies large portions of the horizontal domain, whereas the cold (hot) fluid is localized. Our results suggest that this near-wall statistical distribution of temperature structures, and thus the relative thickness of the kinetic and thermal BLs, does not influence the statistics in the bulk flow state. The reported findings broaden our knowledge of rotating turbulent convection at rather extreme values of the governing parameters and bounded by experimentally realizable boundary conditions, relevant to geo- and astrophysical settings.

Time-delayed feedback control, attributed to Pyragas [Phys. Lett. A 170, 421 (1992)], is a method known to stabilize periodic orbits in low-dimensional chaotic dynamical systems. A system of the form $\dot{\mathit{x}}\left(t\right)=f\left(\mathit{x}\right)$ has an additional term $G\left(\mathit{x}\right(t-T)-\mathit{x}(t\left)\right)$ introduced where $G$ is some “gain matrix” and $T$ a time delay. The form of the delay term is such that it will vanish for any orbit of period $T$, therefore making it also an orbit of the uncontrolled system. This noninvasive feature makes the method attractive for stabilizing exact coherent structures in fluid turbulence. Here we begin by validating the method for the basic flow in Kolmogorov flow; a two-dimensional incompressible Navier-Stokes flow with a sinusoidal body force. The linear predictions for stabilization are well captured by direct numerical simulation. By applying an adaptive method to adjust the streamwise translation of the delay, a known traveling wave solution is able to be stabilized up to relatively high Reynolds number. We discover that the famous “odd-number” limitation of this time-delayed feedback method can be overcome in the fluid problem by using the symmetries of the system. This leads to the discovery of eight additional exact coherent structures which can be stabilized with this approach. This means that certain unstable exact coherent structures can be obtained by simply time stepping a modified set of equations, thus circumventing the usual convergence algorithms.

The purpose of this article is to analyze the large-scale properties of a Richtmyer–Meshkov turbulent mixing zone with large density contrasts and small shock Mach numbers. The main outcome of the study is the expression of a large-scale invariant of the flow. Its existence is contingent on initial conditions but not on the value of the Atwood number which measures the density contrast. As opposed to the small Atwood case, this invariant is not related to the velocity spectrum. Instead, it is given by the value of the spectrum of the solenoidal component of the momentum at small wave numbers. This result stems from the conservation of angular momentum in variable-density flows. Despite this fundamental difference, this invariant still allows to relate the self-similar growth rate of the mixing zone to the large-scale post-shock initial conditions of the flow. Besides, when the shock is weak, this relation can be extended to the pre-shock deformation of the interface. In particular, when the initial interfacial perturbation is limited to small wavelengths (annular spectrum), the growth rate exponent of the mixing zone is shown to saturate to a minimum value close to $1/4$, independently from the Atwood number. The different assumptions and predictions of this work are verified by performing implicit large eddy simulations of a Richtmyer–Meshkov turbulent mixing zone.

The spatial organization of small scales around large-scale coherent structures in a flat plate turbulent boundary layer is studied using a conditional-averaging technique applied to experimental and computational data. The technique averages the small-scale velocity conditioned on the projection coefficient between the instantaneous streamwise velocity field and a model for large-scale velocity structures in the wake and logarithmic regions. Two distinct scenarios are identified for the organization of the small scales: amplitude variation, in which at a given wall-normal location the small-scale intensity varies in amplitude across the streamwise extent of the large-scale structure, and height variation, in which the small-scale velocity intensity remains nearly constant along a curve that changed its wall-normal location across the streamwise extent of the large-scale structure. Small scales that are energetic at the wall-normal location where the large-scale structure is centered primarily show evidence of height variation, while small scales that are energetic at wall-normal locations far from the center of the large-scale structure primarily show evidence of amplitude variation. Connections can be drawn between the statistical observations characterized by the amplitude modulation statistic and the structural picture associated with vortex clusters.

Recent studies have demonstrated the significant roles of droplet self-spin motion in affecting the head-on collision of binary droplets. In this paper, we present a computational study by using the volume-of-fluid method to investigate the spin-affected droplet separation of off-center collisions, which are more probable in reality and phenomenologically richer than head-on collisions. Different separation modes are identified through a parametric study with varying spinning speed and impact parameter. A prominent finding is that increasing the droplet spinning speed tends to suppress the reflexive separation and to promote the stretching separation. Physically, the reflexive separation is suppressed because the increased rotational energy reduces the excessive reflexive kinetic energy within the droplet, which is the cause for the droplet reflexive separation. The stretching separation is promoted because the increased droplet angular momentum enhances the local stretching flow within the droplet, which tends to separate the droplet. The roles of orbital angular momentum and spin angular momentum in affecting the droplet separation are further substantiated by studying the collision between two spinning droplets with either the same or opposite chirality. In addition, a theoretical model based on conservation laws is proposed to qualitatively describe the boundaries of coalescence-separation transition influenced by droplet self-spin motion.

This experimental study examined the effects of controlled vortex generation and interactions created by axisymmetric excitation of a transverse jet, with a focus on the structural and mixing characteristics of the flow. The excitation consisted of a double-pulse forcing waveform applied to the jet, where two distinct temporal square-wave pulses were prescribed during a single forcing period. The two distinct pulses produced vortex rings of different strength and celerity, the strategic selection of which promoted vortex ring interactions or collisions in the near field to varying degrees. Jet flow conditions corresponding to a transitionally convectively and absolutely unstable upstream shear layer (USL) in the absence of forcing, at a jet-to-cross-flow momentum flux ratio of $J=10$, and to an absolutely unstable USL at $J=7$, were explored for a jet Reynolds number of 1800. Acetone planar laser-induced fluorescence imaging was utilized to quantify the influence of different prescribed temporal waveforms. All forcing conditions enhanced the spread, penetration, and molecular mixing of the jet as compared to the unforced jet, though to differing degrees. Interestingly, when the jet was convectively unstable, forcing which promoted vortex collisions provided the greatest enhancement in molecular mixing, whereas the absolutely unstable jet produced the greatest enhancement in mixing when the vortex rings did not interact, with important implications for optimized jet control.

There have been many studies of the instability of a flexible plate or flag to flapping motions, and of large-amplitude flapping. Here we use inviscid simulations and a linearized model to more generally study how key quantities—mode number (or wave number), frequency, and amplitude—depend on the two dimensionless parameters: flag mass and bending stiffness. In the limit of small flag mass, flags perform traveling wave motions that move at nearly the speed of the oncoming flow. The flag mode number scales as the $-1/4$ power of bending stiffness. The flapping frequency has the same scaling, with an additional slight increase with flag mass in the small-mass regime. The flapping amplitude scales approximately as flag mass to the 1/2 power. For large flag mass, the dominant mode number is low (0 or 1), the flapping frequency tends to zero, and the amplitude saturates in the neighborhood of its upper limit (the flag length). In a linearized model, the fastest growing modes have somewhat different power law scalings for wave number and frequency. We discuss how the numerical scalings are consistent with a weakly nonlinear model.

This article presents an experimental description of a jet disturbance occurring during tank draining. This disturbance is visible from the onset of the draining process, and in striking contrast with known jet instabilities, the jet resembles a chain of beads. These beads are generated at the orifice outlet before falling in free fall due to gravity. Such a disturbance is observed for flows through a circular hole, whose size is comparable to the capillary length. This phenomenon is observed when the initial fluid height in the tank exceeds a threshold value. This threshold height depends on the wettability of the outer surface of the tank bottom plate around the outlet orifice. Moreover, this disturbance is more pronounced and lasts longer when the surface around the orifice outlet is hydrophilic. Our experimental results suggest that this disturbance originates from the coupling between turbulence and wetting. Indeed, we believe that this new phenomenon is due to the combination of toroidal vortices generated in the outlet hole and the surface's wettability around the outlet orifice.

Viscous solitons are strongly non-linear surface deformations generated by blowing wind over a liquid beyond a critical viscosity. Their shape and dynamics result from a balance between wind drag, surface tension, and viscous dissipation in the liquid. We investigate here the influence of the liquid viscosity in their generation and propagation. Experiments are carried out using silicon oils, covering a wide range of kinematic viscosities ${\nu }_{\ell }$ between 20 and 5000 ${\mathrm{mm}}^2{\mathrm{s}}^{-1}$. We show that, for ${\nu }_{\ell }>200{\mathrm{mm}}^2{\mathrm{s}}^{-1}$, viscous solitons are subcritically generated from an unstable initial wave train at small fetch, where the wind shear stress is larger. The properties of this initial wave train are those expected from Miles' theory of the Kelvin-Helmholtz instability of a highly viscous fluid sheared by a turbulent wind: the critical friction velocity and critical wavelength are independent of ${\nu }_{\ell }$, and the phase velocity decreases as ${\nu }_{\ell }^{-1}$. We demonstrate the subcritical nature of the transition to viscous solitons by triggering them using a wave maker for a wind velocity below the natural threshold. Finally, we analyze the flow field induced by a viscous soliton, and show that it is well described by a two-dimensional Stokeslet singularity in the far field. The resulting viscous drag implies a propagation velocity with a logarithmic correction in liquid depth, in good agreement with our measurements.

One of the most enigmatic science questions concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number defined as the ratio of turbulent eddy viscosity to particle concentration diffusivity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced as predicted by many existing literature models. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate the turbulent particle diffusivity, while direct measurements and simulations of turbulent particle flux support the occurrence of settling retardation. The analysis presented herein suggests that the value of the turbulent Schmidt number is always larger than unity with values between 3 and 4 based on the directly measured turbulent particle flux. The observed settling reduction cannot be explained by the well-known hindrance effects related to particle concentration. This effect seems to be related to turbulence-particle interactions and correlates more with the Stokes number. Finally, our parameters, namely, the turbulent Schmidt number higher than unity, modified von Kármán constant, and settling retardation, are successfully tested for the modeling of particle concentration profile using the well-known Rouse formulation. This result suggests that alternative parametrizations are possible to reduce the degree of empiricism to predict suspended particle transport by a boundary layer flow.

When two spherical particles submerged in a viscous fluid are subjected to an oscillatory flow, they align themselves perpendicular to the direction of the flow leaving a small gap between them. The formation of this compact structure is attributed to a nonzero residual flow known as steady streaming. We have performed direct numerical simulations of a fully resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. Our simulations show that the particles oscillate both parallel and perpendicular to the oscillating flow in elongated figure-8 trajectories. In absence of bottom friction, the mean gap between the particles depends only on the normalized Stokes boundary layer thickness ${\delta }^{*}$, and on the normalized, streamwise excursion length of the particles relative to the fluid $A_r^{*}$ (equivalent to the Keulegan-Carpenter number). For $A_r^{*}\lesssim 1$, viscous effects dominate and the mean particle separation only depends on ${\delta }^{*}$. For larger $A_r^{*}$ values, advection becomes important and the gap widens. Overall, the normalized mean gap between the particles scales as $L^{*}\approx 3.0{{\delta }^{*}}^{1.5}+0.03{A_r^{*}}^3$, which also agrees well with previous experimental results. The two regimes are also observed in the magnitude of the oscillations of the gap perpendicular to the flow, which increases in the viscous regime and decreases in the advective regime. When bottom friction is considered, particle rotation increases and the gap widens. Our results stress the importance of simulating the particle motion with all its degrees of freedom to accurately model the system and reproduce experimental results. The insights of the particle pairs provide an important step towards understanding denser and more complex systems.

We theoretically investigate the effect of random fluctuations on the motion of elongated microswimmers near hydrodynamic transport barriers in externally driven fluid flows. Focusing on the two-dimensional hyperbolic flow, we consider the effects of translational and rotational diffusion as well as tumbling, i.e., sudden jumps in the swimmer orientation. Regardless of whether diffusion or tumbling are the primary source of fluctuations, we find that noise significantly increases the probability that a swimmer crosses one-way barriers in the flow, which block the swimmer from returning to its initial position. We employ an asymptotic method for calculating the probability density of noisy swimmer trajectories in a given fluid flow, which produces solutions to the time-dependent Fokker-Planck equation in the weak-noise limit. This procedure mirrors the semiclassical approximation in quantum mechanics and similarly involves calculating the least-action paths of a Hamiltonian system derived from the swimmer's Fokker-Planck equation. Using the semiclassical technique, we compute (1) the steady-state orientation distribution of swimmers with rotational diffusion and tumbling and (2) the probability that a diffusive swimmer crosses a one-way barrier. The semiclassical results compare favorably with Monte Carlo calculations.

Reliably predictive simulation of complex flows requires a level of model sophistication and robustness exceeding the capabilities of current Reynolds-averaged Navier-Stokes (RANS) models. The necessary capability can often be provided by well-resolved large eddy simulation (LES), but, for many flows of interest, such simulations are too computationally intensive to be performed routinely. In principle, hybrid RANS/LES (HRL) models capable of transitioning through arbitrary levels of modeled and resolved turbulence would ameliorate both RANS deficiencies and LES expense. However, these HRL approaches have led to a host of unique complications, in addition to those already present in RANS and LES. This work proposes a modeling approach aimed at overcoming such challenges. The approach presented here relies on splitting the turbulence model into three distinct components: two responsible for the standard subgrid model roles of either providing the unresolved stress or dissipation and a third which reduces the model length scale by creating resolved turbulence. This formulation renders blending functions unnecessary in HRL. Further, the split-model approach both reduces the physics-approximation burden on simple eddy-viscosity-based models and provides convenient flexibility in model selection. In regions where the resolution is adequate to support additional turbulence, fluctuations are generated at the smallest locally resolved scales of motion. This active forcing drives the system towards a balance between RANS and grid-resolved LES for any combination of resolution and flow while the split-model formulation prevents local disruption to the total stress. The model is demonstrated on fully developed, incompressible channel flow and the periodic hill, in which it is shown to produce accurate results and avoid common HRL shortcomings, such as model stress depletion.

Stochastic simulations are used to create synthetic one-dimensional telegraph approximation (TA) signals based on turbulent zero crossings, where the interval between crossings is governed by a power-law probability distribution with exponent $\alpha$. The power-law exponent is determined for statistics of simulated TA signals, namely, the box-counting fractal dimension $D_1$, the energy spectrum exponent ${\beta }_{\mathrm{TA}}$, and the intermittency exponent ${\mu }_{\mathrm{TA}}$. For the binary TA signal with no variability in amplitude, the parameters are related linearly as $D_1=2-{\beta }_{\mathrm{TA}}=1-{\mu }_{\mathrm{TA}}$. The relations are unchanged if the crossing interval distribution has a finite power-law region (i.e., inertial subrange) representing a flow with a finite Reynolds number. However, the finite distribution yields statistics that are not truly scale invariant and distorts the linear relation between the statistic exponents and $\alpha$. The behavior is due to finite-size effects apparent from the survival function, or the complementary cumulative distribution, which for finite Reynolds number is only approximately self-similar and has an effective exponent differing from $\alpha$. An expression presented for the effective exponent recovers the expected relations between $\alpha$ and the TA statistics. The findings demonstrate how a finite Reynolds number can affect indicators of self-similarity, fractality, and intermittency observed from single-point measurements.