arXiv subjects

Benjamin Favier

Publications and source records attributed to Benjamin Favier.

At least 37 records · Page 2Linked to original sources

arXiv2021

Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the libration-driven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow mainly consists of a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly non-linear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wave-dominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al, PRL (2017) who introduced the possibility of these two turbulent regimes. The transition between these two regimes and their relevance to geophysical applications are finally discussed.

physics.flu-dyn↗

arXiv2020

Remote determination of the shape of Jupiter's vortices from laboratory experiments

Jupiter's dynamics shapes its cloud patterns but remains largely unknown below this natural observational barrier. Unraveling the underlying three-dimensional flows is thus a primary goal for NASA's ongoing Juno mission that was launched in 2011. Here, we address the dynamics of large Jovian vortices using laboratory experiments complemented by theoretical and numerical analyses. We determine the generic force balance responsible for their three-dimensional pancake-like shape. From this, we define scaling laws for their horizontal and vertical aspect ratios as a function of the ambient rotation, stratification and zonal wind velocity. For the Great Red Spot in particular, our predicted horizontal dimensions agree well with measurements at the cloud level since the Voyager mission in 1979. We additionally predict the Great Red Spot's thickness, inaccessible to direct observation: it has surprisingly remained constant despite the observed horizontal shrinking. Our results now await comparison with upcoming Juno observations.

astro-ph.EP↗

arXiv2020

Gas giant-like zonal jets in the laboratory

This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0015.

physics.flu-dyn↗

arXiv2020

Evidence of the Zakharov-Kolmogorov spectrum in numerical simulations of inertial wave turbulence

Rotating turbulence is commonly known for being dominated by geostrophic vortices that are invariant along the rotation axis and undergo inverse cascade. Yet, it has recently been shown to sustain fully three-dimensional states with a downscale energy cascade. In this letter, we investigate the statistical properties of three-dimensional rotating turbulence by the means of direct numerical simulations in a triply periodic box where geostrophic vortices are specifically damped. The resulting turbulent flow is an inertial wave turbulence that verifies the Zakharov-Kolmogorov spectrum derived analytically by Galtier (Phys. Rev. E, 68, 2003), thus offering numerical proof of the relevance of wave turbulence theory for three-dimensional, anisotropic waves. Lastly, we show that the same forcing leads to either geostrophic or wave turbulence depending on the initial condition. Our results thus bring further evidence for bi-stability in rotating turbulent flows.

physics.flu-dyn↗

arXiv2020

Coupled convection and internal gravity waves excited in water around its density maximum at 4°C

Coupled mixed convective and stratified systems are common in natural flows. To study experimentally the associated dynamics, we use a singular property of water: its non-linear equation of state is characterised by a maximum density close to $4^{\circ}$C. By heating the top of a tank at $35^{\circ}$C and cooling the bottom at $0^{\circ}$C, a two-layer configuration spontaneously appears. The convective motion in the bottom layer consists mostly of a large-scale circulation and rising cold plumes. This turbulent flow generates propagating internal gravity waves in the upper stably-stratified layer. PIV measurements are performed and spectral characteristics of the convection and internal gravity waves are presented. An horizontal large-scale reversing flow in the stratified layer is observed which is viscously driven by a third, intermediate layer. This buffer layer is located between the convective and stratified layers and is thermally coupled with the convective one, hence sustaining a strong horizontal shear. Three dimensional direct numerical simulations with geometry and physical parameters close to the experimental ones corroborate our experimental results.

physics.flu-dyn↗

arXiv2020

Topography generation by melting and freezing in a turbulent shear flow

We report an idealized numerical study of a melting and freezing solid adjacent to a turbulent, buoyancy-affected shear flow, in order to improve our understanding of topography generation by phase changes in the environment. We use the phase-field method to dynamically couple the heat equation for the solid with the Navier-Stokes equations for the fluid. We investigate the evolution of an initially-flat and horizontal solid boundary overlying a pressure-driven turbulent flow. We assume a linear equation of state for the fluid and change the sign of the thermal expansion coefficient, such that the background density stratification is either stable, neutral or unstable. We find that channels aligned with the direction of the mean flow are generated spontaneously by phase changes at the fluid-solid interface. Streamwise vortices in the fluid, the interface topography and the temperature field in the solid influence each other and adjust until a statistical steady state is obtained. The crest-to-trough amplitude of the channels are larger than about 10$δ_ν$ in all cases, with $δ_ν$ the viscous length scale, but are much larger and more persistent for an unstable stratification than for a neutral or stable stratification. This happens because a stable stratification makes the cool melt fluid buoyant such that it shields the channel from further melting, whereas an unstable stratification makes the cool melt fluid sink, inducing further melting by rising hot plumes. The statistics of flow velocities and melt rates are investigated, and we find that channels and keels emerging in our simulations do not significantly change the mean drag coefficient.

physics.flu-dyn↗

arXiv2020

Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance

The dynamics, structure and stability of zonal jets in planetary flows are still poorly understood, especially in terms of coupling with the small-scale turbulent flow. Here, we use an experimental approach to address the questions of zonal jets formation and long-term evolution. A strong and uniform topographic $β$-effect is obtained inside a water-filled rotating tank thanks to the paraboloidal fluid free upper surface combined with a specifically designed bottom plate. A small-scale turbulent forcing is performed by circulating water through the base of the tank. Time-resolving PIV measurements reveal the self-organization of the flow into multiple zonal jets with strong instantaneous signature. We identify a subcritical bifurcation between two regimes of jets depending on the forcing intensity. In the first regime, the jets are steady, weak in amplitude, and directly forced by the local Reynolds stresses due to our forcing. In the second one, we observe highly energetic and dynamic jets of width larger than the forcing scale. An analytical modeling based on the quasi-geostrophic approximation reveals that this subcritical bifurcation results from the resonance between the directly forced Rossby waves and the background zonal flow.

physics.flu-dyn↗

arXiv2020

Improved phase-field models of melting and dissolution in multi-component flows

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes. Phase-field models simplify computation by describing separate regions using a smoothed phase field. The phase field eliminates the need for complicated discretisations that track the moving phase boundary. However standard phase-field models are only first-order accurate. They often incur an error proportional to the thickness of the diffuse interface. We eliminate this dominant error by developing a general framework for asymptotic analysis of diffuse-interface methods in arbitrary geometries. With this framework we can consistently unify previous second-order phase-field models of melting and dissolution and the volume-penalty method for fluid-solid interaction. We finally validate second-order convergence of our model in two comprehensive benchmark problems using the open-source spectral code Dedalus.

physics.comp-ph↗

arXiv2020

Shape and size of large-scale vortices: A generic fluid pattern in geophysical fluid dynamics

Planetary rotation organizes fluid motions into coherent, long-lived swirls, known as large-scale vortices (LSVs), which play an important role in the dynamics and long-term evolution of geophysical and astrophysical fluids. Here, using direct numerical simulations, we show that LSVs in rapidly rotating mixed convective and stably stratified fluids, which approximates the two-layer, turbulent-stratified dynamics of many geophysical and astrophysical fluids, have a generic shape and that their size can be predicted. We show that LSVs emerge in the convection zone from upscale energy transfers and can penetrate into the stratified layer. At the convective-stratified interface, the LSV cores have a positive buoyancy anomaly. Due to the thermal wind constraint, this buoyancy anomaly leads to winds in the stratified layer that decay over a characteristic vertical length scale. Thus LSVs take the shape of a depth-invariant cylinder with a finite-size radius in the turbulent layer and of a penetrating half dome in the stratified layer. Importantly, we demonstrate that when LSVs penetrate all the way through the stratified layer and reach a boundary that is no-slip, they saturate by boundary friction. We provide a prediction for the penetration depth and maximum radius of LSVs as a function of the LSV vorticity, the stratified layer depth, and the stratification. Our results, which apply for cyclonic LSVs, suggest that LSVs in slowly rotating stars and Earth's liquid core are confined to the convective layer, while in Earth's atmosphere and oceans they can penetrate far into the stratified layer.

physics.flu-dyn↗

arXiv2020

Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

We explore the near-resonant interaction of inertial waves with geostrophic modes in rotating fluids via numerical and theoretical analysis. When a single inertial wave is imposed, we find that some geostrophic modes are unstable above a threshold value of the Rossby number $kRo$ based on the wavenumber and wave amplitude. We show this instability to be caused by triadic interaction involving two inertial waves and a geostrophic mode such that the sum of their eigen frequencies is non-zero. We derive theoretical scalings for the growth rate of this near-resonant instability. The growth rate scaled by the global rotation rate is proportional to $(kRo)^2$ at low $kRo$ and transitions to a $kRo$ scaling for larger $kRo$. These scalings are in excellent agreement with direct numerical simulations. This instability could explain recent experimental observations of geostrophic instability driven by waves.

physics.flu-dyn↗

arXiv2020

Robust wall states in rapidly rotating Rayleigh-Bénard convection

We show, using direct numerical simulations with experimentally realizable boundary conditions, that wall modes in Rayleigh-Bénard convection in a rapidly rotating cylinder persist even very far from their linear onset. These nonlinear wall states survive in the presence of turbulence in the bulk and are robust with respect to changes in the shape of the boundary of the container. In this sense these modes behave much like the topologically protected states present in two-dimensional chiral systems even though rotating convection is a three-dimensional nonlinear driven dissipative system. We suggest that the robustness of this nonlinear mode may provide an explanation for the strong zonal flows observed recently in simulations and experiments on rapidly rotating convection at high Rayleigh number.

physics.flu-dyn↗

arXiv2020

Bistability in Rayleigh-Bénard convection with a melting boundary

A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and solid phases appears. Depending on the initial conditions, freezing or melting occurs until the interface eventually converges towards a stationary state. This evolution is studied numerically in a two-dimensional configuration using a phase-field method coupled with the Navier-Stokes equations. Varying the control parameters of the model, we exhibit two types of equilibria: diffusive and convective. In the latter case, Rayleigh-Bénard convection in the liquid phase shapes the solid-liquid front, and a macroscopic topography is observed. A simple way of predicting these equilibrium positions is discussed and then compared with the numerical simulations. In some parameter regimes, we show that multiple equilibria can coexist depending on the initial conditions. We also demonstrate that, in this bi-stable regime, transitioning from the diffusive to the convective equilibrium is inherently a nonlinear mechanism involving finite-amplitude perturbations.

physics.flu-dyn↗

arXiv2019

Low-frequency variability in massive stars: Core generation or surface phenomenon?

Bowman et al. (2019) reported low-frequency photometric variability in 164 O- and B-type stars observed with K2 and TESS. They interpret these motions as internal gravity waves, which could be excited stochastically by convection in the cores of these stars. The detection of internal gravity waves in massive stars would help distinguish between massive stars with convective or radiative cores, determine core size, and would provide important constraints on massive star structure and evolution. In this work, we study the observational signature of internal gravity waves generated by core convection. We calculate the \textit{wave transfer function}, which links the internal gravity wave amplitude at the base of the radiative zone to the surface luminosity variation. This transfer function varies by many orders of magnitude for frequencies $\lesssim 1 \, {\rm d}^{-1}$, and has regularly-spaced peaks near $1 \, {\rm d}^{-1}$ due to standing modes. This is inconsistent with the observed spectra which have smooth ``red noise'' profiles, without the predicted regularly-spaced peaks. The wave transfer function is only meaningful if the waves stay predominately linear. We next show that this is the case: low frequency traveling waves do not break unless their luminosity exceeds the radiative luminosity of the star; and, the observed luminosity fluctuations at high frequencies are so small that standing modes would be stable to nonlinear instability. These simple calculations suggest that the observed low-frequency photometric variability in massive stars is not due to internal gravity waves generated in the core of these stars. We finish with a discussion of (sub)surface convection, which produces low-frequency variability in low-mass stars, very similar to that observed in Bowman et al. (2019) in higher mass stars.

astro-ph.SR↗

arXiv2019

Subcritical turbulent condensate in rapidly rotating Rayleigh-Bénard convection

The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows.

physics.flu-dyn↗

arXiv2019

Rayleigh-Bénard convection with a melting boundary

We study the evolution of a melting front between the solid and liquid phases of a pure incompressible material where fluid motions are driven by unstable temperature gradients. In a plane layer geometry, this can be seen as classical Rayleigh-Bénard convection where the upper solid boundary is allowed to melt due to the heat flux brought by the fluid underneath. This free-boundary problem is studied numerically in two dimensions using a phase-field approach, classically used to study the melting and solidification of alloys, which we dynamically couple with the Navier-Stokes equations in the Boussinesq approximation. The advantage of this approach is that it requires only moderate modifications of classical numerical methods. We focus on the case where the solid is initially nearly isothermal, so that the evolution of the topography is related to the inhomogeneous heat flux from thermal convection, and does not depend on the conduction problem in the solid. From a very thin stable layer of fluid, convection cells appears as the depth -- and therefore the effective Rayleigh number of the layer increases. The continuous melting of the solid leads to dynamical transitions between different convection cell sizes and topography amplitudes. The Nusselt number can be larger than its value for a planar upper boundary, due to the feedback of the topography on the flow, which can stabilize large-scale laminar convection cells.

physics.flu-dyn↗

arXiv2018

Turbulent kinematic dynamos in ellipsoids driven by mechanical forcing

Dynamo action in planetary cores has been extensively studied in the context of convectively-driven flows. We show in this letter that mechanical forcings, namely tides, libration and precession, are also able to kinematically sustain a magnetic field against ohmic diffusion. Previous attempts published in the literature focused on the laminar response or considered idealized spherical configurations. In contrast, we focus here on the developed turbulent regime and we self-consistently solve the magnetohydrodynamic (MHD) equations in an ellipsoidal container. Our results open new avenues of research in dynamo theory where both convection and mechanical forcing can play a role, independently or simultaneously.

physics.flu-dyn↗

arXiv2018

The energy flux spectrum of internal waves generated by turbulent convection

We present three-dimensional direct numerical simulations of internal waves excited by turbulent convection in a self-consistent, Boussinesq and Cartesian model of convective--stably-stratified fluids. We demonstrate that in the limit of large Rayleigh number ($Ra\in [4\times 10^7,10^9]$) and large stratification (Brunt-Väisälä frequencies $f_N \gg f_c$, where $f_c$ is the convective frequency), simulations are in good agreement with a theory that assumes waves are generated by Reynolds stresses due to eddies in the turbulent region (Lecoanet \& Quataert 2013 MNRAS 430 (3) 2363-2376). Specifically, we demonstrate that the wave energy flux spectrum scales like $k_{\perp}^4f^{-13/2}$ for weakly-damped waves (with $k_{\perp}$ and $f$ the waves' horizontal wavenumbers and frequencies), and that the total wave energy flux decays with $z$, the distance from the convective region, like $z^{-13/8}$.

physics.flu-dyn↗

arXiv2018

Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves

We demonstrate via direct numerical simulations that a periodic, oscillating mean flow spontaneously develops from turbulently generated internal waves. We consider a minimal physical model where the fluid self-organizes in a convective layer adjacent to a stably stratified one. Internal waves are excited by turbulent convective motions, then nonlinearly interact to produce a mean flow reversing on timescales much longer than the waves' period. Our results demonstrate for the first time that the three-scale dynamics due to convection, waves, and mean flow is generic and hence can occur in many astrophysical and geophysical fluids. We discuss efforts to reproduce the mean flow in reduced models, where the turbulence is bypassed. We demonstrate that wave intermittency, resulting from the chaotic nature of convection, plays a key role in the mean-flow dynamics, which thus cannot be captured using only second-order statistics of the turbulent motions.

physics.flu-dyn↗