Designated a new cloud feature in 2017, asperitas clouds are wave-like formations on the underside of layer clouds. We propose a mechanism for asperitas cloud formation: an instability driven by the settling and evaporation of water droplets. For suitable droplet size and liquid water content, a layer of dense air forms, which in moderate ambient shear gives rise to cloud structures of the asperitas type.

In climate predictions, clouds are the leading source of uncertainty. For both predictions and basic understanding, a main challenge is to account for the vast range of scales, from the scales of individual clouds to the large-scale circulations. Here, an idealized simulation framework is investigated with stochastic clouds, so that some clouds are not subgrid-scale and are instead evolving on the numerical grid, albeit stochastically. The results show the possibility of following the influence of clouds on climate in idealized climate change simulations.

In this article we bridge between the Rayleigh-Bénard convection literature and the atmospheric literature by expressing the governing equations for cloudy convection in a dimensionless form. The governing parameters are Rayleigh, Prandtl, Schmidt, Damköhler, and sedimentation numbers for the cloudy case. We further connect to the atmospheric literature by obtaining an expression for the Nusselt number (dimensionless heat flux) for a cloud–convection system, directly from the conservation equations for temperature and water vapor, and illustrate the microphysics independence through large eddy simulation of an idealized cloudy Rayleigh-Bénard convection flow.

Rotating thermal convection captures key properties of geophysical and astrophysical systems. By performing high-resolution direct numerical simulations we strongly connect the physics of wall-localized states of rotating convection with observations of a boundary zonal flow where turbulent convection has a strong boundary localized structure with similar properties. We show that as buoyancy increases at fixed rotation rate, spatial, temporal, and heat-transport properties of the localized state change smoothly and monotonically. Our results connect the physics of rotating convection in finite containers with similar geophysical/astrophysical phenomena at much larger spatial scales.

Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. In this paper, we design bubbles made of a composite liquid film able to neutralize all these effects and keep their integrity for more than one year in a standard atmosphere.

Shear-induced migration is ubiquitous in a suspension of solid and soft particles. The contribution to particle deformability and frictional contacts between particles needs to be clarified. By measuring normal forces with viscous resuspension experiments of frictionless droplets, we show droplet deformation does not play a significant role, contrary to frictional contacts, as the normal force is much weaker for droplets than for solid particles at high volume fractions.

In transition pipe flow, when the flow is driven by a constant pressure gradient, it can enter a regime where the Reynolds number varies sinusoidally and the intermittent patches of turbulence appear periodically. Ludwig Prandtl and Oskar Tietjens proposed a qualitative explanation for this phenomenon, but their mechanism has never before been put to a quantitative test. Combining extensive experiments and modeling, we find quantitative agreement between the Prandtl-Tietjens mechanism and experimental observations, and show that this oscillating regime exists for all flows where both the pressure gradient and perturbation are constant.

This work examines how a fluid-fluid interface can not be considered infinitely narrow within fluid fragmentation. A set of self-similar equations is obtained and resolved for the jet pinching-off as the finite-thickness of the interface becomes the characteristic radial size. This approach can lead to further understanding of physical phenomena involving free-surface flows close to the nanoscale, for example, in structural biology with XFEL or aerospace thrusters.

Heterogeneous coexistence turbulence (HCT) with anisotropic wave turbulence and isotropic vortex turbulence includes a transition range beyond the application limits of cascade theory and weak turbulence theory. Local-flux vectors, formulated based on scalar potential functions, of conserved quantities in the wavenumber space quantify their directional properties. Two balance types, time and term, make up the idea of critical balance, which the proposed local-flux vectors can quantitatively evaluate. The local-flux vectors reveal anisotropic fluxes along the wavenumbers deduced from the critical balance as well as energy-enstrophy double cascade in HCT of Charney-Hasegawa-Mima model.

Compliance in fluid carrying vessels is the capability of interacting with flow and attenuating waves via mechanisms such as the Windkessel effect. In this paper we investigate how vessel compliance impacts the dynamics of flow and pressure in the transient regime shortly after changes in boundary conditions. We show that individual vessels as well as networks composed of many such vessels can exist in one of two possible regimes, one in which transient dynamics are fast and one in which it is slow. These results can be used to analyze the response capabilities of biological flow networks such as the animal vasculature.

We present a detailed study of the three-dimensional two-way fluid-structure interactions between viscous blood plasma and the hyperelastic solid nanofibers comprising the Endothelial Glycocalyx Layer, along with a simple analytical model. Examining the elasto-hydrodynamics under startup shear and pulsatile flow conditions, we shed light on mesoscopic events close to microvessel walls under physiologic conditions. Our findings impact the efficiency of paracellular and transcellular transport of biological molecules, plasma ions, and viruses. We correlate macroscopic properties like permeability to dimensionless terms, which can expand possible uses to similarly structured hairy networks.

Tracers immersed in suspensions of microswimmers such as bacteria or algae display several phenomena unseen in equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value. Previous theoretical studies have focussed on spherical tracers undergoing isotropic diffusion. Here, we present a computational model of ellipsoidal tracer particles undergoing anisotropic diffusion due to a collection of microswimmers. Our results show that the anisotropic translational diffusion due to microswimmers is qualitatively different from the corresponding equilibrium case, and occurs only for microswimmer concentrations where correlations are significant.

Accurately calculating pairwise collisions between swimming microorganisms typically requires the use of numerical simulations in which hydrodynamic interactions are fully resolved. Here, we utilize analytical expressions for forces and torques acting on two closely separated spherical squirmers to evaluate their scattering dynamics and bound states, by varying incoming angles, the squirmer parameter β, and gravitational field strengths. These results compare well with full numerical solutions obtained using boundary element methods, highlighting lubrication theory as a candidate for use in future mesoscale continuum models.

The role of mechanistic (free-slip or non-slip) and thermal (adiabatic or isothermal) wall conditions on flame acceleration at the early stages of burning in channels is studied by computational simulations of the reacting flow equations involving fully compressible hydrodynamics and transport properties (heat conduction, diffusion and viscosity). A qualitatively new effect is observed in the case of isothermal walls preheated to a high temperature. Specifically, additional flame segments are formed near a wall in that case, leading eventually to emergence and propagation of an intriguing octopus-like flame front.

Unsteady translation of a sphere in a viscoelastic fluid is studied analytically. General, fully invertible relationships between an imposed time-dependent velocity and the resultant force are described in terms of a Volterra series expansion. These results are used to analyze particle motion in fluids described by the Johnson-Segalman and Giesekus models and to define a general framework for analyzing weakly nonlinear microrheology measurements.

We present results from direct numerical simulations of rotating Rayleigh–B\’enard convection (RRBC), the quintessential paradigm for investigating buoyancy-driven rotating turbulence, at rather extreme values of the governing parameters and bounded by experimentally realizable no-slip boundary conditions. We provide a statistical characterization of the RRBC flow regimes that can be used as a framework for identification of these flow states in future experiments and simulations at even more extreme parameter values, and for extrapolation to geophysical and astrophysical flow systems.

Thermal convection in a nonrotating spherical shell with central gravity is known to have symmetric solutions in terms of three-dimensional discrete rotation. All the solutions have reflection symmetry. We found a new type of symmetric steady convection with chirality. The pattern consists of six pairs of spiral rolls placed on 12 faces of a regular spherical dodecahedron. There are two configurations that are mirror images of one another.

A droplet will be reflected like a light beam when it impacts obliquely on a horizontal solid surface. In the present work, whether or not the droplet obeys the so-called ‘reflection law’ like a light beam is numerically explored. It is found that the reflection angle is always larger than the incident angle as the magnitudes of the normal and tangential velocities reduce disproportionately after reflection. Specifically, the normal restitution coefficient (${ϵ}^n$) satisfies the general scaling relationship of ${ϵ}^n$ ~ We${}^{-1/4}$ for moderate normal Weber number We while the tangential restitution coefficient (${ϵ}^t$) scatters around a constant value.

When a bubble bursts at the surface of a liquid, it produces a jet that may break up into several droplets which play a key role in the exchange between the air and the ocean. Here, we show how the velocity and the size of those droplets are robust to the initial conditions.

A volume-of-fluid (VOF) based numerical study on the spin-affected droplet separation of off-center collisions is presented. The roles of orbital angular momentum $L_o$ and spin angular momentum $L_s$ in affecting the droplet separation are illustrated by changing the chirality of droplet spin, showing that an augmented total angular momentum can promote the stretching separation and suppress the reflexive separation. A unified theoretical model based on conservation laws is proposed to qualitatively describe the boundaries of the coalescence-separation transition influenced by droplet self-spin motion.

The interaction between two immiscible droplets in a confined shear flow is studied numerically by using a ternary diffuse-interface model. Three different types of interaction are observed: (1) reverse motion, (2) pass-over motion, and (3) rotary Janus motion after wetting. We investigate the effects of initial droplet position, capillary number, and confinement on the droplet trajectory and the deformation.

The electrohydrodynamic interactions between multiple and dissimilar drops are measured experimentally, and a pairwise electrohydrodynamic theory to describe the drop interactions is presented. The trajectories of three and four interacting drops are shown to be qualitatevly predicted by the theory. Drops with distinct electrical properties exhibit nonreciprocal interactions, and the same drop pair can undergo opposite trajectories with different initial separation distances.

The nanofluidic paradigm that low-concentration conductance is concentration-independent has recently come under scrutiny. Recent works have shown that the conductance depends on the concentration and that the slope, $\alpha$, ranges between 0 and $1/2$. However, experiments have also measured slopes of $2/3$ and 1. In this work an analytical solution for the conductance is derived that accounts for surface charge regulation (SCR), advection (ADV), and slip-lengths (SL). This parameter free model demonstrates that $\alpha$ is determined by SCR, ADV, SL, and ranges between 0 and 1. Consequently our results imply that all three phenomena are essential in the design of nanofluidic systems.

Electrohydrodynamics of a compound drop migrating in a plane Poiseuille flow under the influence of a uniform electric field is studied using a double asymptotic method for the concentric case and a semi-analytical approach for the eccentric situation. The effect of viscosity, conductivity, and permittivity ratios, and the applied electric field’s orientation and radius ratio is thoroughly investigated. The underlying physics is examined in terms of surface charge distribution and shape deformation.

Volumetrically heated jets mimic fluid flow in cloudy plumes, and the entrainment rate coefficient in such jets can vary significantly along the axial direction. In this work, we formulate an energy consistent Gaussian integral model for volumetrically heated jets, in which the entrainment rate coefficient is dynamically evolved along the axis. The widths for radial profiles of velocity, tracer concentration, and temperature are allowed to evolve separately. The results from the model agree reasonably well with corresponding integral statistics obtained from Large Eddy Simulations.

When a shear flow delivers sufficient stress to a granular bed, bed particles will start to erode. It has long been known that the critical stress required to initiate sediment transport depends on the shear history of the bed, and that beds tend to strengthen in response to weak flow. We find here that this strengthening effect is highly directional, in that beds only become stronger against flows oriented in the same direction as the conditioning flow. In fact, we find that conditioned beds are actually significantly weaker against flows oriented in other directions, with significant implications for predictions of sediment transport.

The immiscible displacement of a viscous fluid by a less viscous one in a porous medium is known to be unstable and often results in dendritic fingering patterns, where the pressure gradient is screened internally and only advanced invading parts grow. We present experiments in porous media, systematically varying the imposed injection pressure ($P$) and viscosity ratio ($M$) of the invading to defending fluid. A crossover to more stable and compact invasion structures is found for higher $P$ and $M$. This compact invasion regime onset is observed even for $M<{10}^{-3}$. We show that the pressure gradient is not screened in this regime and invasion patterns exhibit rich internal flow dynamics.

This experimental study examines the effects of controlled vortex generation and interactions on a round transverse jet for a range of jet-to-crossflow momentum flux ratios. Utilizing acetone planar laser-induced fluorescence (PLIF) imaging, alterations in jet structure, penetration, and molecular mixing created by such vortical interactions are quantified. Differences are found to depend on the state of the natural instabilities in the jet’s upstream shear layer, with implications for jet control strategies.

The flutter of a thin flexible plate or flag is a benchmark problem in fluid-structure interactions with applications to energy harvesting and flow sensing. Here we study flutter dynamics across a wide range of bending stiffnesses, and down to very small values of flag mass, e.g. very flexible fabric flags. We find that the flapping amplitude, frequency, and wavenumber are power laws of the flag mass and stiffness.

At specific operating conditions, especially at large print gap heights, the airflow in the print gap of inkjet printers can become unstable and misplace the satellite droplets on the paper. Two-dimensional numerical analyses are performed to shed light into the dynamics of the vortex in the print-zone and determine the range of flow regimes at different conditions. This will provide a refined understanding of the two-dimensional mode of oscillation while characterizing the upper bound at which the base flow meets the conditions for a uniform print.

This work presents an alternative formulation of resolvent analysis based on the calculus of variations. The proposed formulation circumvents reliance on inversion of the linear operator and is inherently compatible with any arbitrary choice of norm. Several examples are presented which highlight the analytical and numerical advantages and limitations of the proposed formulation.

In this experimental study, by interferometry, we characterize the structure of a liquid film, draining due to gravity, on a vertical, narrow substrate. The surface tension effects affect the draining film from the two vertical edges, and eventually influence the shape over the entire width.

A jet disturbance starting at the onset of the flow occurs during the draining of a tank through an orifice whose size is comparable to the capillary length. This paper presents an experimental investigation of this phenomenon, which is not one of the known jet instabilities. 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.

When wind blows over a highly viscous liquid, localized liquid bumps, of height of the order of the capillary length, are generated and propagate downwind. These strongly nonlinear coherent structures, called “viscous solitons”, contrast with the weakly nonlinear waves observed at low viscosity. Our experiments performed at different liquid viscosities demonstrate that viscous solitons arise subcritically from unstable Kelvin-Helmholtz waves generated at small fetch.

We replace the classical two-phase Leidenfrost effect with a three-phase system: ice and its meltwater levitating on water vapor. The critical Leidenfrost temperature, which is about 150 °C for water droplets on smooth aluminum, increased to about 550 °C for ice disks. This results in an order of magnitude increase in heat flux from 150–550 °C, suggesting that ice quenching may be a superior alternative to spray quenching for firefighting, metallurgy, and preventing pressure buildup in nuclear reactors.

Coherent strucutres of m = 1 are investigated via microgravity and terrestrial experiments in thermocapillary-driven convection in half-zone liquid bridge of high Prandtl number. Individual behaviors of low Stokes number particles are monitored in the laboratory frame and the rotating frame of reference to illustrate the correlation between the coherent structure and the thermal flow field induced by the hydrothermal wave instability.

Drag force models generally used in Eulerian-Lagrangian (EL) methods only represent the mean hydrodynamic force acting upon a suspension; higher-order drag force statistics, arising from neighbor-induced flow perturbations, are neglected, affecting particle velocity variance and dispersion predictions. We develop a force Langevin (FL) model that treats neighbor-induced drag fluctuations as a stochastic process. The stochastic EL framework specifies unresolved drag force statistics, leading to the correct evolution of particle velocity variance over a wide range of Reynolds numbers and solids volume fractions, when compared to particle-resolved DNS of freely evolving homogeneous suspensions.

Stratification inhibits the development of particle clusters due to upflows that develop between the descending particles. However, particles do become more vertically aligned if the background diffusivity is smaller.

Statistical descriptions of inertial particle motion are complicated by the random and multiscale structure of the turbulent velocity field. In this paper, we develop a stochastic model for inertial particles on the basis of “filtered” fluid tracer particles. Introducing an effective Stokes number allows us to capture crucial features of inertial particle motion such as the sharp decrease of acceleration variance for increasing Stokes numbers (acceleration trajectories are color-coded by maximum tracer acceleration). The proposed modeling approach could yield further insights on preferential concentration and a better experimental characterization of particle-laden flows.

We propose a pore network extraction method based on the concept of omnidirectional Euclidean distance (OED) so as to extract the accurate pore network structures of porous media with pores of high aspect ratios. A deterministic method is introduced to identify the pore body and the pore throat regions. The proposed extraction method is validated by comparing the pore network modeling results against the direct numerical simulation results and the experimental data. The proposed pore network extraction method not only preserves the topological and morphological properties of the void spaces in porous media but also is robust and insensitive to the image noise.

Using coupled granular-fluid simulations we study the particle size segregation and diffusion in sheared granular flows immersed in different ambient fluids. Both segregation and diffusion decrease with the fluid viscosity but only after exceeding a certain threshold value. Decreasing the relative density between the particles and the fluid further slows down segregation but does not significantly affect diffusion. Empirical relationships for the segregation velocity and diffusion coefficient are developed in terms of the Stokes number which are used to model the segregation-diffusion process across different types of fluids.

Drying in porous media is characterized by the fragmentation of the liquid phase in many evolving clusters. Here, a drying model is presented considering explicitly the fragmentation process within the framework of the continuum approach to porous media. The model is extended so as to predict the evolution of a solute in the fragmented liquid phase during drying.

When solid particles, such as sediments, are transported by a turbulent boundary layer flow, the wall-normal turbulent diffusion of particle concentration has been observed to be much higher than the turbulent diffusion of momentum (the eddy viscosity). This is characterized by a turbulent Schmidt number lower than unity. By using the few available existing direct measurements of Reynolds-averaged wall-normal particle flux and our two-phase flow large eddy simulations we demonstrate that the actual turbulent Schmidt number is indeed higher than unity. The misinterpretation may be explained by settling retardation of particles in turbulent flows compared with quiescent water.

When two identical spherical particles are submerged in an oscillating fluid, they align themselves perpendicularly to the direction of the flow, leaving a small gap between them. The formation of this structure is attributed to a non-zero residual flow known as steady streaming. We performed direct numerical simulations of a fully resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. In equilibrium, the particles oscillate both parallel and perpendicularly to the oscillating flow. Two scaling regimes for the particle dynamics, which are related to changes in the (average) flow field, are observed.

A granular droplet that is composed of smaller and denser particles in a bed of larger and lighter particles is found to sink and split when subjected to a combination of vibration and fluidizing gas flow. Despite visual similarities with fluid-like instabilities, the observed phenomenon is a result of the particulate character of granular matter. Combining experiments and numerical simulations, we show that the droplet of high-density particles causes the formation of an immobilized zone that obstructs the downwards motion of the droplet and causes the droplet to spread and ultimately to split. We further investigate the conditions required for droplet splitting.

The trajectories of microswimmers, such as plankton or artificial active particles, are altered by their interactions with the ambient flow. We show here that microswimmers swimming beneath surface gravity waves can resurface or swim to deep depths depending on their coupling to the flow. We obtain a system of equations describing wave-averaged microswimmer trajectories, from which we calculate the probability of reaching the surface as a function of swimming speed and body shape.

Using machine learning, we find a simple yet efficient strategy for microswimmers to actively adjust their swimming direction in response to hydromechanical signals, allowing robust vertical migration in turbulence. In contrast, passive bottom-heavy swimmers migrate much slower upwards and settle much slower downwards. Our results may be important to understand daily long-range vertical migration of plankton in the turbulent ocean, or to engineer efficient strategies for fabricated microswimmers.

Nonlinear travelling waves and equilibria are stabilized from two-dimensional Navier-Stokes turbulence using time-delayed feedback. This is achieved by time-stepping a modified set of equations and, as such, avoids performing costly root-finding iterations. Using underlying symmetries enables the stabilization of several solutions, some at high Reynolds number. No other special properties of the solution need to be known in advance.

The suppression of chaotic acoustic oscillations is a challenging problem in optimization. This is because gradient-based optimization struggles to optimize chaotic systems. In this paper, we develop a Bayesian approach based on reservoir computing to suppress chaotic oscillations without calculating the gradient.

The trajectories of self-propelled particles, i.e. swimmers, in prescribed fluid flows are fundamentally altered by translational and rotational noise, especially in the vicinity of transport barriers. We devise a technique for calculating the probability of specific paths of noisy swimmers in a flow. Our approach provides insights into the swimmer trajectories and accurately quantifies the position-dependent swimmer transport rate in a hyperbolic flow.

This work analyzes the Taylor dispersion of elongated rods in a two-dimensional Poiseuille flow between parallel, rigid walls at small and large rotational Peclet numbers. Asymptotic expressions for the dispersivity and mean advection speed in these limits are derived. The approach could be used to analyze dispersion of rods in other types of unidirectional flows.

This work aims to estimate the time-resolved velocity field that is directly associated with pressure fluctuations in a subsonic round jet. Synchronous measurements of the velocity field and in-flow pressure fluctuations were performed on streamwise and cross-stream measurement planes. The spectral linear stochastic estimation and neural network architectures were implemented to estimate time-resolved velocity fields. In all cases, pressure fluctuations inside the flow are found to be connected to the streamwise convection of large-scale coherent structures in the flow, and the unique advantage of the bidirectional long-short-time-memory (LSTM) method is also reported in this work.

An instantaneous streamwise velocity perturbation of a new simulation of a turbulent channel flow at an unprecedented friction Reynolds number of 10000 is conducted. One point statistics and turbulent budgets are discussed, solving some questions and raising new ones.

Hybrid RANS/LES models, capable of transitioning through arbitrary levels of modeled and resolved turbulence, aim to ameliorate both RANS deficiencies and LES expense. We propose a method combining active forcing of the resolved flow field, where appropriate, with splitting the standard single turbulence model into separate models, responsible for either the unresolved stress or dissipation, which adapts to turbulence that $is$ resolved as opposed to turbulence one $wants$ to be resolved. In this way, a “consistent” LES is constructed, in that it observes both RANS and DNS limits and remains valid for levels of resolution where the majority of the turbulent stress is not resolved.

Single-point measurements of turbulent flows are often reduced to a binary zero-crossing signal to investigate parameters related to self-similarity, fractality, and intermittency. The present stochastic simulations demonstrate the influence of a finite Reynolds number on the apparent scale-dependence of power law exponents for these parameters. The behavior is a statistical consequence of finite-size effects created by a limited range of scales exhibiting a power law.

The spectral analysis of the large scales of Richtmyer-Meshkov turbulent mixing zones is extended to the case of high density-contrasts. Large-scale invariants are derived and shown to determine the growth rate of the mixing zone.

We study the organization of large- and small-scale velocity motions in a boundary layer using a new conditional projection averaging technique. Large-scale structures are found to correlate to both the amplitude and position of strong small-scale velocity intensity in the boundary layer. Different amplitude and position effects are found depending on the region of the boundary layer and the small-scale velocity component considered.

In turbulent bluff body flows, the presence of vortex shedding, a form of coherent structures, introduces a new characteristic scale that is distinct from the scale of background stochastic turbulence. This double-scale picture essentially invalidates the conventional single-scale modeling for the turbulence energy dissipation in steady-RANS simulations. This paper presents a conceptual model to quantify the uncertainty in the steady-RANS dissipation closure for flows past bluff bodies with vortex shedding.

Temperature transformation does not collapse data, but the resulting wall model accurately predicts temperatures in high-speed boundary layer flows. Here we explain why this is so. The insights gained lead to a new turbulent Prandtl number formulation and more accurate wall models.

Small scale intermittency is ubiquitous in turbulent flows. Many features of small-scale motions can be described by the velocity gradient tensor (VGT) for which the nonlinear term in the Navier-Stokes equations (NSE) is a source of strong fluctuations. The figure shows intermittent time signals of longitudinal VGT elements along Lagrangian trajectories from five levels of a recently proposed nested multiple time-scale model (MTSM), partly derived from NSE. We show that a single level of MTSM valid at moderate Reynolds numbers (Re) can generate valid statistics and scaling exponents for arbitrarily high Re. Excellent agreement with direct numerical simulation and experimental data is found.

A novel nonintrusive optical wave gauge is developed to simultaneously measure three components of the wave field. The synchronous single point measurement of temporal variation of surface elevation and its orthogonal slope components allowed us to estimate directional spectra. Unlike in field experiments, where the directional wave spreading is affected also by variation in the wind direction, in a laboratory facility the wind is unidirectional thus allowing characterization of directional spreading as an intrinsic property of wind waves.

Surface wave dynamics in small scale configurations can be substantially modified by edge constraints, in particular a pinned contact line, when the force it exerts is non-negligible with respect to gravity and surface tension. This work develops a hybrid approach, which combines a theoretical model with a complete space-time resolved measurement of the surface deformation and static menisci, allowing an accurate estimation of the contribution of a pinned contact line to shift the dispersion relation towards faster phase velocities.

Faraday waves are created in experiment with spatial structure that conforms to the cylindrical container geometry and is defined by the mode number pair ($n,\ell$). The shape of the instability tongue in the frequency-acceleration space depends upon the edge conditions, filling depth, and liquid properties.

Three-layer stratified shear flows provide an excellent opportunity to study the interaction between fluid-fluid interfaces. In this paper we explore this coupling by studying a pair of nonlinear evolution equations derived in the limit of strong surface tension. The addition of a third fluid, hence a second interface, destabilizes the linearized system, and we use a numerical approach to simulate the resulting disturbance growth. A range of nonlinear phenomena are subsequently observed which include stable traveling waves, droplet formation of the middle fluid, quasi-periodicity, and coarsening phenomena, as shown in the key image.