arXiv subjects

Basile Gallet

Publications and source records attributed to Basile Gallet.

At least 19 recordsLinked to original sources

arXiv2026

Surface gravity wave-mean flow interaction with comparable spatial scales. Part I: reduced wave equations

We consider deep-water surface gravity waves propagating above a background flow whose spatial scale is comparable to the wavelength, focusing on the regime where the flow is slow compared to the group velocity of the waves. We introduce an "equivalent solvability condition" method to construct reduced equations, demanding that, upon multiple-timescale expansion, the reduced equations share the same leading-order solution and first solvability condition as the original system. This approach turns the full 3D problem into a 2D reduced equation for the wave field. We derive such reduced equations for broad-band waves above a depth-invariant background flow, and for narrow-band waves above a fully 3D background flow. In the latter case the reduced equation takes the form of a Schrodinger equation involving the near-surface vorticity of the background flow only, with the impact of the near-surface horizontal flow divergence shown to be subdominant. Beyond the reduction in spatial dimensionality, the latter reduced equation describes the evolution of the wave field over the slow advective timescale of the background flow, thereby eliminating the computational burden of time-resolving the fast wave period. We illustrate the capabilities of the reduced equations through an analytical solution for the weak scattering of a wave packet by a patch of organized flow, followed by numerical solutions for stronger scattering of a wave packet by a patch of disorganized flow.

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arXiv2026

Surface gravity wave-mean flow interaction with comparable spatial scales. Part II: two-way coupling and wave-wave interactions

We consider narrow-band deep-water surface gravity waves propagating above a background flow whose spatial scale is comparable to the wavelength. We focus on the regime where the background-flow speed is comparable to the Stokes drift of the waves to derive a two-way coupled model between the fast waves and the slow background flow. Nonlinear wave interactions arise at the same asymptotic order as the two-way coupling and must therefore be included in the derivation. The resulting model consists of a nonlinear version of the reduced wave equation obtained in part I, coupled to a Craik-Leibovich equation governing the evolution of the background flow. The model describes the evolution of the wave field and background flow over the slow turnover frequency of the background flow, thus saving the computational burden of temporally resolving the fast wave frequency. The inviscid model exactly conserves wave action, mechanical energy and horizontal momentum, while the viscous model exactly conserves horizontal momentum. The coupling terms are cast in compact form for ease of physical interpretation and numerical implementation.

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arXiv2026

Equilibrium statistical mechanics of waves in inhomogeneous moving media

We adapt the microcanonical framework of equilibrium statistical mechanics to predict the statistics of short waves in inhomogeneous moving media. For steady inhomogeneities and background flow, we compute the wave spectrum at any location in the domain based on an ergodic prescription for the action density in phase space, constrained by conservation of absolute frequency. We illustrate the method for shallow-water waves subject to a background flow or to topographic inhomogeneities, and for deep-water surface capillary waves over a background flow, validating the predicted maps of rms surface elevation and interfacial slope against numerical simulations.

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arXiv2026

Complex dynamical regimes of the Tayler-Spruit dynamo

Astrophysical dynamos feature various spatial structures and dynamical regimes, ranging from hemispherical magnetic fields to the random reversals of the geodynamo. The recently observed Tayler-Spruit dynamo has been invoked to explain angular momentum transport in stellar radiative zones and magnetar formation in a proto-neutron star spun-up by fallback accretion. Whether this dynamo mechanism can lead to different dynamical regimes remains an open question. Using three-dimensional direct numerical simulations, we model the dynamics of a stably stratified spherical Couette flow, with the outer sphere rotating faster than the inner one. While the generation of strong stationary and hemispherical dynamos has been observed in our previous studies, we report for the first time the existence of reversals and complex temporal dynamics. We observe that the dynamics is strongly correlated with the equatorial symmetry breaking of the flow. Focusing on a fiducial dynamo simulation, we propose a simple interpretation of its dynamics, which consists in the coupling of two large-scale magnetic modes with two opposite equatorial symmetries by the flow symmetry breaking. While this interpretation captures the simplest observed dynamics, the nonlinear interaction between a higher number of magnetic modes is certainly required to describe some of the more complex regimes. The wide diversity of dynamical regimes generated by the Tayler-Spruit dynamo may have interesting implications for the geometry of the neutron star magnetic fields, and therefore neutron star emissions.

astro-ph.HE↗

arXiv2025

Quantitatively mapping the Eady model onto a two-layer quasi-geostrophic model

The two-layer quasigeostrophic model (2LQG) and the Eady model are two idealized systems illustrating the baroclinic instability of atmospheric jets and ocean currents. The two setups share many ingredients -- background vertically sheared zonal flow of density-stratified fluid in a rapidly rotating frame -- while differing in complexity and dimensionality. The Eady model has a continuous vertical direction, with baroclinic turbulence induced by boundary potential vorticity (PV) gradients at top and bottom. By contrast, the 2LQG sytem typically models baroclinic instability induced by interior PV gradients. This distinction challenges our ability to clearly identify a couple of 'modes' through which the Eady dynamics could be inferred from a simpler 2LQG system. In the present study, we show that this difficulty can be circumvented in the turbulent regime arising for weak bottom drag. Namely, guided by the common organization of both systems into a gas of coherent vortices, we identify a quantitative mapping between the Eady and the 2LQG models. The mapping allows for parameter-free predictions of the eddy diffusivity of the Eady model based on the knowledge of the 2LQG diffusivity. We illustrate these results using numerical simulations of the Eady and 2LQG models with linear or quadratic bottom drag.

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arXiv2025

Statistics of near-inertial waves over a background flow via quantum and statistical mechanics

We revisit the interaction of an initially uniform near-inertial wave (NIW) field with a steady background flow, with the goal of predicting the subsequent organization of the wave field. To wit, we introduce an exact analogy between the Young Ben Jelloul (YBJ) equation and the quantum dynamics of a charged particle in a steady electromagnetic field, whose potentials are expressed in terms of the background flow. We derive the time-averaged spatial distributions of wave kinetic energy, potential energy and Stokes drift in two asymptotic limits. In the `strongly quantum' limit where the background flow is weak compared to wave dispersion, we compute the wave statistics by extending a strong-dispersion expansion initially introduced by YBJ. In the `quasi-classical' limit where the background flow is strong compared to wave dispersion, we compute the wave statistics by leveraging the equilibrium statistical mechanics of classical systems. We compare our predictions to numerical simulations of the YBJ equation, using an instantaneous snapshot from a two-dimensional turbulent flow as the steady background flow. The agreement is very good in both limits. In particular, we quantitatively describe the preferential concentration of NIW energy in anticyclones. We predict weak NIW concentration in both asymptotic limits of weak and strong background flow, and maximal anticyclonic concentration for background flows of intermediate strength, providing theoretical underpinning to observations reported by Danioux, Vanneste and B\"uhler (Journal of Fluid Mechanics, 773, 2015).

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arXiv2024

Effective transport by 2D turbulence: Vortex-gas theory vs. scale-invariant inverse cascade

The scale-invariant inverse energy cascade is a hallmark of 2D turbulence, with its theoretical energy spectrum observed in both direct numerical simulations (DNS) and laboratory experiments. Under this scale-invariance assumption, the effective diffusivity of a 2D turbulent flow is dimensionally controlled by the energy flux and the friction coefficient only. Surprisingly, however, we show that such scaling predictions are invalidated by numerical solutions of the 2D Navier-Stokes equation forced at intermediate wave number and damped by weak linear or quadratic drag. We derive alternate scaling-laws for the effective diffusivity based on the emergence of intense, isolated vortices causing spatially inhomogeneous frictional dissipation localized within the small vortex cores. The predictions quantitatively match DNS data. This study points to a universal large-scale organization of 2D turbulent flows in physical space, bridging standard 2D Navier-Stokes turbulence with large-scale geophysical turbulence.

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arXiv2024

Two-layer baroclinic turbulence with arbitrary layer depths

While heat transport by baroclinic turbulence in oceans and planetary atmospheres is well described by a two-layer model, the relative depth of the two layers varies greatly depending on the situation of interest, making it an important parameter governing the transport properties of the system. Focusing on the low-drag turbulent regime, we extend the vortex-gas scaling theory to address the case of arbitrary layer depths. To wit, we map the arbitrary-layer-depth system onto an equivalent equal-depth system with rescaled parameters, establishing the asymptotic validity of the mapping for weak bottom drag. This approach leads to quantitative predictions for the turbulent transport by two-layer baroclinic turbulence with arbitrary layer depths, without additional free parameters. We validate these predictions using an extended suite of numerical simulations with either linear or quadratic bottom drag.

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arXiv2024

Numerical validation of the inverse cascade of surface gravity wave action

We report numerical simulations of surface gravity waves forced at small scale and the subsequent inverse cascade of wave action. We combine the spectral approach to simulating weakly nonlinear waves with the capabilities of modern Graphics Processing Units to reach unprecedented scale separation between the forcing and domain scales. The resulting broad inertial range allows for an unambiguous confirmation of the theoretical prediction for the spectrum in the inverse cascade regime, both in terms of spectral index and dependence of the spectral level on the action flux.

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arXiv2024

Two-dimensional turbulence above topography: condensation transition and selection of minimum enstrophy solutions

We consider two-dimensional flows above topography, revisiting the selective decay (or minimum-enstrophy) hypothesis of Bretherton and Haidvogel. We derive a 'condensed branch' of solutions to the variational problem where a domain-scale condensate coexists with a flow at the (smaller) scale of the topography. The condensate arises through a supercritical bifurcation as the conserved energy of the initial condition exceeds a threshold value, a prediction that we quantitatively validate using Direct Numerical Simulations (DNS). We then consider the forced-dissipative case, showing how weak forcing and dissipation select a single dissipative state out of the continuum of solutions to the energy-conserving system predicted by selective decay. As the forcing strength increases, the condensate arises through a supercritical bifurcation for topographic-scale forcing and through a subcritical bifurcation for domain-scale forcing, both predictions being quantitatively validated by DNS. This method provides a way of determining the equilibrated state of forced-dissipative flows based on variational approaches to the associated energy-conserving system, such as the statistical mechanics of 2D flows or selective decay.

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arXiv2024

Rapidly rotating radiatively driven convection: experimental and numerical validation of the `geostrophic turbulence' scaling predictions

We experimentally and numerically characterize rapidly rotating radiatively driven thermal convection, beyond the sole heat transport measurements reported in Bouillaut et al. (2021). Based on a suite of direct numerical simulations (DNS) and additional processing of the experimental data collected by Bouillaut et al. (2021), we report the simultaneous validation of the scaling predictions of the `geostrophic turbulence' regime -- the diffusivity-free or `ultimate' regime of rapidly rotating convection -- for the heat transport, the temperature fluctuations, the flow speed and the flow structure. Radiatively driven convection thus appears as a versatile setup for the laboratory observation of the diffusivity-free regimes of various convective flows of geophysical and/or astrophysical interest.

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arXiv2023

Vortex core radius in baroclinic turbulence: Implications for scaling predictions

We revisit the vortex-gas scaling theory for heat transport by baroclinic turbulence based on the empirical observation that the vortex core radius departs from the Rossby deformation radius for very low bottom drag coefficient. We derive a scaling prediction for the vortex-core radius. For linear bottom drag this scaling dependence for the vortex-core radius does not affect the vortex-gas predictions for the eddy diffusivity and mixing-length, which remain identical to those in Gallet and Ferrari (Proc. Nat. Acad. Sci. USA, 117, 2020). By contrast, for quadratic drag the scaling dependence of the core radius induces new scaling-laws for the eddy diffusivity and mixing length when the quadratic-drag coefficient becomes asymptotically low. We validate the modified scaling predictions through numerical simulations of the two-layer model with very low quadratic-drag coefficient.

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arXiv2023

Vertical structure of buoyancy transport by ocean baroclinic turbulence

Ocean mesoscale eddies enhance meridional buoyancy transport, notably in the Antarctic Circumpolar Current where they contribute to setting the deep stratification of the neighboring ocean basins. The much-needed parameterization of this buoyancy transport in global climate models requires a theory for the overall flux, but also for its vertical structure inside the fluid column. Based on the quasi-geostrophic dynamics of an idealized patch of ocean hosting an arbitrary vertically sheared zonal flow, we provide a quantitative prediction for the vertical structure of the buoyancy flux without adjustable parameters. The prediction agrees quantitatively with meridional flux profiles obtained through numerical simulations of an idealized patch of ocean with realistic parameter values. This work empowers modelers with an explicit and physically based expression for the vertical profile of buoyancy transport by ocean baroclinic turbulence, as opposed to the common practice of using arbitrary prescriptions for the depth-dependence of the transport coefficients.

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arXiv2023

A direct derivation of the Gent-McWilliams/Redi diffusion tensor from quasi-geostrophic dynamics

The transport induced by ocean mesoscale eddies remains unresolved in most state-of-the-art climate models and needs to be parameterized instead. The natural scale separation between the forcing and the emergent turbulent flow calls for a diffusive parameterization, where the eddy-induced fluxes are related to the large-scale gradients by a diffusion tensor. The standard parameterization scheme in climate modeling consists in adopting the Gent-McWilliams/Redi (GM/R) form for the diffusion tensor, initially put forward based on physical intuition and educated guesses before being put on firm analytical footing using thickness-weighted average (TWA). In the present contribution we provide a direct derivation of this diffusion tensor from the quasi-geostrophic (QG) dynamics of a horizontally homogeneous three-dimensional patch of ocean hosting a large-scale vertically-sheared zonal flow on the beta plane. While less general than the TWA approach, the present QG framework leads to rigorous constraints on the diffusion tensor. First, there is no diapycnal diffusivity arising in the QG GM/R tensor for low viscosity and small-scale diffusivities. The diffusion tensor then involves only two vertically dependent coefficients, namely the GM transport coefficient $K_{GM}(z)$ and the Redi diffusivity $K_R(z)$. Secondly, as already identified by previous authors the vertical structures of the two coefficients are related by the so-called Taylor-Bretherton relation. Finally, while the two coefficients generically differ in the interior of the water column, we show that they are equal to one another near the surface and near the bottom of the domain for low-enough dissipative coefficients. We illustrate these findings by numerically simulating the QG dynamics of a horizontally homogeneous patch of ocean hosting a vertically sheared zonal current resembling the Antarctic Circumpolar Current.

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arXiv2022

Velocity-informed upper bounds on the convective heat transport induced by internal heat sources and sinks

Three-dimensional convection driven by internal heat sources and sinks (CISS) leads to experimental and numerical scaling-laws compatible with a mixing-length - or `ultimate' - scaling regime $Nu \sim \sqrt{Ra}$. However, asymptotic analytic solutions and idealized 2D simulations have shown that laminar flow solutions can transport heat even more efficiently, with $Nu \sim Ra$. The turbulent nature of the flow thus has a profound impact on its transport properties. In the present contribution we give this statement a precise mathematical sense. We show that the Nusselt number maximized over all solutions is bounded from above by const.$\times Ra$, before restricting attention to 'fully turbulent branches of solutions', defined as families of solutions characterized by a finite nonzero limit of the dissipation coefficient at large driving amplitude. Maximization of $Nu$ over such branches of solutions yields the better upper-bound $Nu \lesssim \sqrt{Ra}$. We then provide 3D numerical and experimental data of CISS compatible with a finite limiting value of the dissipation coefficient at large driving amplitude. It thus seems that CISS achieves the maximal heat transport scaling over fully turbulent solutions.

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arXiv2022

MRI-driven dynamo at very high magnetic Prandtl numbers

The dynamo driven by the magnetorotational instability (MRI) is believed to play an important role in the dynamics of accretion discs and may also explain the origin of the extreme magnetic fields present in magnetars. Its saturation level is an important open question known to be particularly sensitive to the diffusive processes through the magnetic Prandtl number Pm (the ratio of viscosity to resistivity). Despite its relevance to proto-neutron stars and neutron star merger remnants, the numerically challenging regime of high Pm is still largely unknown. Using zero-net flux shearing box simulations in the incompressible approximation, we studied MRI-driven dynamos at unprecedentedly high values of Pm reaching 256. The simulations show that the stress and turbulent energies are proportional to Pm up to moderately high values ($\mathrm{Pm} \sim 50$). At higher Pm, they transition to a new regime consistent with a plateau independent of Pm for $\rm Pm \gtrsim 100$. This trend is independent of the Reynolds number, which may suggest an asymptotic regime where the energy injection and dissipation are independent of the diffusive processes. Interestingly, large values of Pm not only lead to intense small-scale magnetic fields but also to a more efficient dynamo at the largest scales of the box.

astro-ph.HE↗

arXiv2022

Experimental observation of the geostrophic turbulence regime of rapidly rotating convection

The competition between turbulent convection and global rotation in planetary and stellar interiors governs the transport of heat and tracers, as well as magnetic-field generation. These objects operate in dynamical regimes ranging from weakly rotating convection to the `geostrophic turbulence' regime of rapidly rotating convection. However, the latter regime has remained elusive in the laboratory, despite a worldwide effort to design ever-taller rotating convection cells over the last decade. Building on a recent experimental approach where convection is driven radiatively, we report heat transport measurements in quantitative agreement with this scaling regime, the experimental scaling-law being validated against direct numerical simulations (DNS) of the idealized setup. The scaling exponent from both experiments and DNS agrees well with the geostrophic turbulence prediction. The prefactor of the scaling-law is greater than the one diagnosed in previous idealized numerical studies, pointing to an unexpected sensitivity of the heat transport efficiency to the precise distribution of heat sources and sinks, which greatly varies from planets to stars.

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arXiv2022

Effective drag in rotating, poorly conducting plasma turbulence

Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large time-scale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parametrizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background magnetic field. We find that the drag parametrization fails once the time-scale associated with the Lorentz force becomes shorter than the dynamical time-scale in the system, beyond which the effective drag coefficient remains roughly constant, despite orders-of-magnitude variation in the Lorentz (magnetic) time-scale. We offer an improvement to the drag parametrization by considering the relevant asymptotic limit of low conductivity and strong background magnetic field, known as the quasi-static MHD approximation of the Lorentz force. This approximation removes the fast time-scale associated with magnetic diffusion, but retains a more complex version of the Lorentz force, which could be utilized in future numerical models of hot Jupiter atmospheric circulation.

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