The turbulence of capillary waves on the surface of a ferrofluid with a high permeability in a horizontal magnetic field is considered in the framework of a one-dimensional weakly nonlinear model. In the limit of a strong magnetic field, the surface waves under study can propagate without distortions along or against the direction of external field, i.e., similar to Alfvén waves in a perfectly conducting fluid. The interaction of counter-propagating nonlinear waves leads to the development of wave turbulence on the surface of the liquid. The computational data show that the spectrum of turbulence is divided into two parts: a low-frequency dispersionless region, where the magnetic forces dominate and a high-frequency dispersive one, in which the influence of capillary forces becomes significant. In the first region, the spectrum of the surface elevation has the same exponent in $k$ and $ω$ domains and its value is close to $-3.5$, what is in a good agreement with the estimation obtained from the dimensional analysis of the weak turbulence spectra. At the high frequencies, the computed spatial spectrum of the surface waves is close to $k^{-5/2}$ which corresponds to $ω^{-5/3}$ in terms of the frequency. This spectrum does not coincide with the Zakharov-Filonenko spectrum obtained for pure capillary waves. A possible explanation of this fact is in the influence of coherent structures (like shock waves) usually arising in media with weak dispersion.
It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detai…
The linear stability analysis of the Faraday instability on a viscous ferrofluid in a horizontal magnetic field is performed. Strong dipole-dipole interactions lead to the formation of chains elongated in the field direction. The formation of chains results in a qualitative new behaviour of the ferrofluid. This new behaviour is characterized by a neutral stability curve similar to that observed earlier for Maxwell viscoelastic liquids and causes a significant weakening of the energy dissipation at high frequencies. In the case of a ferrofluid with chains in a horizontal magnetic field, the eff…
In ferrofluids the suspended ferromagnetic particles agglomerate due to the interaction between the particle magnetic moment and the external magnetic field, which in turn, influences the turbulence and relaxation time. The relaxation time becomes large when we are considering turbulence drag force instead of viscous drag force in Brownian motion. We investigate that the total energy conservation in ferrofluids taking into interaction between the external magnetic field and the ferrofluid.
We report observations of wave turbulence on the surface of a ferrofluid submitted to a magnetic field parallel to the fluid surface. The magnetic wave turbulence shows several differences compared to the normal field case reported recently. The inertial zone of the magnetic wave turbulence regime is notably found to be strongly increased with respect to the normal field case, and to be well described by our theoretical predictions. The dispersion relation of linear waves is also measured and differs from the normal field case due to the absence of the Rosensweig instability.
We report the observation of wave turbulence on the surface of a ferrofluid mechanically forced and submitted to a static normal magnetic field. We show that magnetic surface waves arise only above a critical field. The power spectrum of their amplitudes displays a frequency-power law leading to the observation of a magnetic wave turbulence regime which is experimentally shown to involve a 4-wave interaction process. The existence of the regimes of gravity, magnetic and capillary wave turbulence is reported in the phase space parameters as well as a triple point of coexistence of these three r…
The spontaneous motion of liquid droplets on solid surfaces is the result of an unbalanced surface tension force, which is sometimes called the "Marangoni effect". This can be triggered by either a difference in surface temperature or a heterogeneity in the topography or chemistry of the surface passively or actively. The imbibition of liquid within capillary tubes, horizontal ice wicking on either hydrophilic or hydrophobic substrates, and inkjet printing for example are just some classic illustrations of where the Lucas-Washburn equation can predict droplet behavior characteristics fairly we…
We consider turbulence in a stratified 'Kolmogorov' flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratifica- tion is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connec…
The atmosphere is a nonlinear stratified fluid in which internal gravity waves are present. These waves interact with the flow, resulting in wave turbulence that displays important differences with the turbulence observed in isotropic and homogeneous flows. We study numerically the role of these waves and their interaction with the large scale flow, consisting of vertically sheared horizontal winds. We calculate their space and time resolved energy spectrum (a four-dimensional spectrum), and show that most of the energy is concentrated along a dispersion relation that is Doppler shifted by the…
We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in the horizontal direction is a combination of a continuous-time eddy-constrained random walk process with a contribution to transport from horizontal winds. Transport at times larger than the Lagrangian turnover time is not universal and dependent on these winds. The models yield results in good agreement with direct numerical simulations of stratified turbu…
Lagrangian statistics of passive tracers in rotating turbulence is investigated by Particle Tracking Velocimetry. A confined and steadily-forced turbulent flow is subjected to five different rotation rates. The PDFs of the velocity components clearly reveal the anisotropy induced by background rotation. Although the statistical properties of the horizontal turbulent flow field are approximately isotropic, in agreement with previously reported results by van Bokhoven and coworkers [Phys. Fluids 21, 096601 (2009)], the velocity component parallel to the (vertical) rotation axis gets strongly red…
We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths. The results broaden the scope of recent findings on Faraday waves in thin …
This review paper is devoted to a presentation of recent progress in wave turbulence. I first present the context and state of the art of this field of research both experimentally and theoretically. I then focus on the case of wave turbulence on the surface of a fluid, and I discuss the main results obtained by our group: caracterization of the gravity and capillary wave turbulence regimes, the first observation of intermittency in wave turbulence, the occurrence of strong fluctuations of injected power in the fluid, the observation of a pure capillary wave turbulence in low gravity environme…
The complex interaction between turbulence and the free surface in boundary layer shear flow created by a vertical surface-piercing wall is considered. A laboratory-scale device was built that utilizes a surface-piercing stainless steel belt that travels in a loop around two vertical rollers, with one length of the belt between the rollers acting as a horizontally-moving flat wall. The belt is accelerated suddenly from rest until reaching constant speed in order to create a temporally-evolving boundary layer analogous to the spatially-evolving boundary layer that would exist along a surface-pi…
We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [Moffatt, JFM 28, 1967]. However, numerous numerical studies predict a different behaviour, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using Direct Numerica…
We present laboratory experiments of surface wave turbulence excited by paddles in the deep water regime. The free surface is seeded with buoyant particles that are advected and dispersed by the flow. Positions and velocities of the floaters are measured using particle tracking velocimetry. We study the statistics of velocity and acceleration of the particles, mean vertical displacements, single-particle horizontal dispersion, and the phenomenon of preferential concentration. Using a simple model together with the experimental data, we show that the time evolution of the particles has three ch…
Vertically banded zonal jets are frequently observed in weakly or non-rotating stratified turbulence, with the quasi-biennial oscillation in the equatorial stratosphere and the ocean's equatorial deep jets being two examples. Explaining the formation of jets in stratified turbulence is a fundamental problem in geophysical fluid dynamics. Statistical state dynamics (SSD) provides powerful methods for analyzing turbulent systems exhibiting emergent organization, such as banded jets. In SSD, dynamical equations are written directly for the evolution of the turbulence statistics, enabling direct a…
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Re…
We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps which continuously injects velocity fluctuations towards the center of a rotating water tank. The energy transfers are evaluated from two-point third-order three-component velocity structure functions, which we measure using stereoscopic particle image velocimetry in the rotating frame. Without global rotation, the energy is transferred from large to small scales, as in classical three-dimensional turbulence. Fo…
We experimentally study the role of the forcing on gravity-capillary wave turbulence. Previous laboratory experiments using spatially localized forcing (vibrating blades) have shown that the frequency power-law exponent of the gravity wave spectrum depends on the forcing parameters. By horizontally vibrating the whole container, we observe a spectrum exponent that does not depend on the forcing parameters for both gravity and capillary regimes. This spatially extended forcing leads to a gravity spectrum exponent in better agreement with the theory than by using a spatially localized forcing. T…
We employ the horizontal visibility algorithm to map the velocity and acceleration time series in turbulent flows with different Reynolds numbers, onto complex networks. The universal nature of velocity fluctuations in high Reynolds turbulent Helium flow is found to be inherited in the corresponding network topology. The degree distributions of the acceleration series are shown to have stretched exponential forms with the Reynolds number dependent fitting parameter. Furthermore, for acceleration time series, we find a transitional behavior in terms of the Reynolds number in all network feature…
Stratified flows forced by internal waves similar to those obtained in the Coriolis platform (LEGI, Grenoble, France) \cite{Savaro2020} are studied by pseudospectral triply-periodic simulations. The experimental forcing mechanism consisting in large oscillating vertical panels is mimicked by a penalization method. The analysis of temporal and spatiotemporal spectra reveals that the flow for the strongest forcing in the experiments is composed of two superposed large and quasi-steady horizontal vortices, of internal waves in box modes and of much weaker waves outside the modes. Spatial spectra …
The statistical properties of the Lagrangian acceleration vector of passive tracers in statistically-steady rotating turbulence is studied by Particle Tracking Velocimetry. Direct effects of the background rotation are the suppression of high-acceleration events parallel to the (vertical) rotation axis, the enhancement of high-acceleration events for the horizontal acceleration, and the strong amplification of the auto-correlation of the acceleration component perpendicular to both the rotation vector Ω and local velocity vector u. The auto-correlation of the acceleration component in the plan…
Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the processes push parcels towards saturation. Numerical simulations demonstrate the emergence of a moist turbulent state consisting of ordered structures with a clear power-law type spectral scaling from initially spatially uncorrelated conditions. An asymptotic analysis in the limit of rapid condensation and strong stratification shows that, for initial conditions…
Turbulent mixing in the radiative regions of stars is usually either ignored or crudely accounted for in most stellar evolution models. However, there is growing theoretical and observational evidence that such mixing is present and can affect various aspects of a star's life. In this work, we present a first attempt at quantifying mixing by horizontal shear instabilities in stars using Direct Numerical Simulations. The shear is driven by a body force, and rapidly becomes unstable. At saturation, we find that several distinct dynamical regimes exist, depending on the relative importance of str…
Direct numerical simulation of threedimensional chaotic motion of a dielectric liquid with a free surface under the action of external horizontal electric field is carried out. The numerical model takes into account the effects of surface tension, viscosity, and external isotropic random forcing acting at large scales. A transition from dispersive capillary wave turbulence to quasi-isotropic nondispersive EHD surface turbulence with increase of the external electric field strength is numerically observed for the first time. At the regime of developed EHD wave turbulence, the total electrical e…
This article investigates penetrative turbulence in the atmospheric boundary layer. Using a large eddy simulation approach, we study characteristics of the mixed layer with respect to surface heat flux variations in the range from 231.48 W/m$^2$ to 925.92 W/m$^2$, and observe that the surface heterogeneity on a spatial scale of $20$ km leads to downscale turbulent kinetic energy cascade. Coherent fluctuations of mesoscale horizontal wind is observed at 100m above the ground. Such a surface induced temporal oscillations in the horizontal wind suggest a rapid jump in mesocale wind forecasts, whi…
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, focusing on cases where the frequencies associated with rotation and stratification (RaS), $N$ and $f$ respectively, are held at a fixed ratio $N/f=5$. As the intensity of RaS increases, a sharp transition is observed between a regime dominated by eddies to a regime dominated by waves, which can also be seem…
We study the generation of 2D turbulence in Faraday waves by investigating the creation of spatially periodic vortices in this system. Measurements which couple a diffusing light imaging technique and particle tracking algorithms allow the simultaneous observation of the three-dimensional fluid motion and of the temporal changes in the wave field topography. Quasi-standing waves are found to coexist with a spatially extended fluid transport. More specifically, the destruction of regular patterns of oscillons coincides with the emergence of a complex fluid motion whose statistics are similar to…
We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and…
The combined effectiveness of model reduction and the quasilinear approximation for the reproduction of the low-order statistics of oceanic surface boundary-layer turbulence is investigated. Idealized horizontally homogeneous problems of surface-forced thermal convection and Langmuir turbulence are studied in detail. Model reduction is achieved with a Galerkin projection of the governing equations onto an subset of modes determined by proper orthogonal decomposition. For less than 0.2% of the modes retained, the reduced quasilinear model is able to reproduce vertical profiles of horizontal mea…
We analyze the dynamics of small particles vertically confined, by means of a linear restoring force, to move within a horizontal fluid slab in a three-dimensional (3D) homogeneous isotropic turbulent velocity field. The model that we introduce and study is possibly the simplest description for the dynamics of small aquatic organisms that, due to swimming, active regulation of their buoyancy, or any other mechanism, maintain themselves in a shallow horizontal layer below the free surface of oceans or lakes. By varying the strength of the restoring force, we are able to control the thickness of…
Numerical models of the flow and wakes due to turbines operating within a real-scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade-resolved simulations. With the introduction of turbine parametrizations such as the actuator disk (AD) or the actuator line (AL) models, this problem has been partially addressed, yet the computational cost associated with these simulations remains high. In this work, we present an implementation and validation of an AL model within the mesh-adaptive three-dimensional fluid dynamics solver, Fluidity, un…
Stratification can cause turbulence spectra to deviate from Kolmogorov's isotropic -5/3 power-law scaling in the universal equilibrium range at high Reynolds numbers. However, a consensus has not been reached with regard to the exact shape of the spectra. Here we propose a theoretically-derived shape of the turbulent kinetic energy (TKE) and temperature spectra in horizontal wavenumber that consists of three regimes at small Froude number: the buoyancy subrange, a transition region and isotropic inertial subrange through derivation based on previous research. These regimes are confirmed by var…
The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of low magnetic Reynolds number. DNS and LES computations are performed for two values of the hydrodynamic Reynolds number (10^4 and 2\times 10^4) and the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near …
In this paper, we investigate the statistical features of the fully developed, forced, rapidly rotating, {turbulent} system using numerical simulations, and model {the} energy {spectrum} that {fits} well with the numerical data. Among the wavenumbers ($k$) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionized energy spectrum is ${\bar E}({\bar k})\approx \exp(-0.05{\bar k})$, where overbar denotes appropriate non-dimensionalization. {For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more th…
This work describes an experimental investigation on the mixing induced by a swarm of high Reynolds number air bubbles rising through a nearly homogeneous and isotropic turbulent flow. The gas volume fraction $α$ and the velocity fluctuations $u'_0$ of the carrier flow before bubble injection are varied, respectively, in the ranges $0\leq α\leq 0.93\%$ and 2.3 cm/s $\leq u'_0 \leq 5.5$ cm/s, resulting in a variation of the bubblance parameter $b$ in the range [0, 1.3] ($b = \frac{V_r^2 α}{{u'}_0^2}$, where $V_r$ is the relative rising velocity). Mixing in the horizontal direction can be modell…
The solar tachocline is a shear layer located at the base of the solar convection zone. The horizontal shear in the tachocline is likely turbulent, and it is often assumed that this turbulence would be strongly anisotropic as a result of the local stratification. What role this turbulence plays in the tachocline dynamics, however, remains to be determined. In particular, it is not clear whether it would result in a turbulent eddy diffusivity, or anti-diffusivity, or something else entirely. In this paper, we present the first direct numerical simulations of turbulence in horizontal shear flows…
In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to $\sim 10^{-3}$, and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes $(\pm1,0,0)$ and $(0,\pm1,0)$ that correspond to the largest columnar structure in the flow. For wavenumbers ($k$) greater than the enstrophy dissipation…
The scattering of inertia-gravity waves by large-scale geostrophic turbulence in a rapidly rotating, strongly stratified fluid leads to the diffusion of wave energy on the constant-frequency cone in wavenumber space. We derive the corresponding diffusion equation and relate its diffusivity to the wave characteristics and the energy spectrum of the turbulent flow. We check the predictions of this equation against numerical simulations of the three-dimensional Boussinesq equations in initial-value and forced scenarios with horizontally isotropic wave and flow fields. In the forced case, wavenumb…
Statistically stationary and homogeneous shear turbulence (SS-HST) is investigated by means of a new direct numerical simulation code, spectral in the two horizontal directions and compact-finite-differences in the direction of the shear. No remeshing is used to impose the shear-periodic boundary condition. The influence of the geometry of the computational box is explored. Since HST has no characteristic outer length scale and tends to fill the computational domain, long-term simulations of HST are `minimal' in the sense of containing on average only a few large-scale structures. It is found …
The vectoral wind structure of daytime atmospheric boundary layer (ABL) turbulence is strongly dependent on the balance between shear-driven turbulence production of horizontal fluctuations (driven by winds at the mesoscale), and buoyancy-driven turbulence production of vertical velocity fluctuations (driven by solar heating), characterized by the global instability state parameter $-z_i/L > 0$. In the fully shear-driven neutral limit $-z_i/L \rightarrow 0$, the surface layer is dominated by coherent streamwise-elongated concentrations of negative streamwise fluctuating velocity (low-speed str…
We present a simple, new criterion to extract line plumes from the velocity fields, without using the temperature field, in a horizontal plane close to the plate in turbulent convection. The existing coherent structure detection criteria from velocity fields, proposed for shear driven wall turbulence, are first shown to be inadequate for turbulent convection. Based on physical arguments, we then propose that the negative values of $\overline{\nabla_H}\cdot\overline{u}$, the horizontal divergence of the horizontal velocity field extracts the plume regions from the velocity field. The $\overline…
We present the first demonstration of the negative effective magnetic pressure instability in direct numerical simulations of stably stratified, externally forced, isothermal hydromagnetic turbulence in the regime of large plasma beta. By the action of this instability, an initially uniform horizontal magnetic field forms flux concentrations whose scale is large compared to the turbulent scale. We further show that the magnetic energy of these large-scale structures is only weakly dependent on the magnetic Reynolds number, provided its value is large enough for the instability to be excited. O…
