arXiv subjects

Benjamin Favier

Publications and source records attributed to Benjamin Favier.

At least 19 recordsLinked to original sources

arXiv2026

Relative dispersion and eddy diffusivity in laboratory experiments of $\beta$-plane turbulence

We present the first experimental measures of relative dispersion and turbulent diffusion in rapidly-rotating turbulence in the zonostrophic regime, i.e., in the presence of instantaneous and dominant zonal jets. Synthetic Lagrangian trajectories are computed from time-resolved experimental velocity fields, from which we measure relative (two-particle) dispersion. Time-based and separation-based statistics are calculated, including the cumulative inverse separation time (CIST), for which analytical predictions exist in the inertial ranges (direct enstrophy cascade and inverse energy cascade) and in the diffusive regime. These statistics show evidence of a transition from a Richardson regime at scales larger than the energy-injection scale, to a diffusive regime, at scales larger than the transitional scale, the scale at which turbulence becomes anisotropic due to the interaction between turbulent eddies and Rossby waves. The analytical predictions for the CIST allow us to measure the turbulent energy dissipation rate in the Richardson regime, and the turbulent diffusivity in the diffusive regime. Our measurements of diffusivity are broadly consistent with predictions from mixing-length and zonostrophic theories but suggest a shallower dependence on the energy dissipation rate.

physics.flu-dyn↗

arXiv2026

Meltwater transport and mixing layer growth near the ice--ocean interface

Ice melting into saline water plays a fundamental role in the dynamics near the ice-ocean interface in polar oceans. The physics of ice melting involves a non-trivial interplay between thermodynamics at the interface, hydrodynamic transport in the bulk and the properties of the ambient ocean. The key control parameters are the density ratio $R_\rho$ proportional to the ambient ocean salinity and the Lewis number $Le = \kappa_T/\kappa_S$, which compares the thermal and salt diffusivities. Increasing the salinity is known to slow down melting, with the melt rate transitioning from subdiffusive to diffusive as $R_\rho$ increases. Here, we ssess the role of turbulence in this transition, using highly-resolved numerical simulations of the two-dimensional Boussinesq equations with a slowly melting upper boundary. We analyse the non-stationary growth of the temperature and meltwater mixing layers, varying the Lewis number and the density ratio. While meltwater is continuously entrained by convection inside the bulk, we identify a transition from convection to diffusion close to the interface. This transition is reflected by the formation of an interfacial boundary layer that regulates the flux of meltwater pouring into the turbulent bulk for $R_\rho \gtrsim 10$. Using mixing-layer diagnostics based on meltwater-concentration thresholds, we observe that the turbulent layer grows super-diffusively $\propto t^{1.33}$, while the interfacial boundary layer expands diffusively $\propto t^{0.5}$ but with a non-universal prefactor. These results indicate that double-diffusive effects are here confined to the interface, and highlight potential limitations of diagnostics based on fixed concentration thresholds in oceanographic applications.

physics.flu-dyn↗

arXiv2026

Zonal flows driven by libration in rotating spherical shells: the case of periodic characteristic paths

This work investigates the weakly nonlinear dynamics of internal shear layers and the mean zonal flow induced by the longitudinal libration of an inner core within a spherical shell. Building on the work of He et al. (J. Fluid Mech., vol. 939, 2022, A3), which focused on linear dynamics, we adopt a similar setup to explore the nonlinear regime using both asymptotic theory and numerical computations, with Ekman numbers as low as $E=10^{-10}$. A specific forcing frequency of $\widehat{\omega}=\sqrt{2}\widehat{\Omega}$, where $\widehat{\Omega}$ denotes the rotation rate, is introduced to generate a closed rectangular path of characteristics for the inertial wave beam generated at the critical latitude. Our approach extends previous results by Le Diz\`es (J. Fluid Mech., vol. 899, 2020, A21) and reveals that nonlinear interactions are predominantly localized around regions where the wave beam reflects on the boundary. We derive specific scaling laws governing the nonlinear interactions: the width of the interaction region scales as $E^{1/3}$, and the amplitude of the resulting mean zonal flow scales as $E^{1/6}$ in general. However, near the rotation axis, where the singularity of the self-similar solution becomes more pronounced, the amplitude exhibits a scaling of $E^{-1/2}$. In addition, our study also examines the nonlinear interactions of beams which are governed by different scaling laws. Through comparison with numerical results, we validate the theoretical predictions of the asymptotic framework, observing good agreement as the Ekman number decreases.

physics.flu-dyn↗

arXiv2025

Instability triggered by mixed convection in a thin fluid layer

We investigate the convective stability of a thin, infinite fluid layer with a rectangular cross-section, subject to imposed heat fluxes at the top and bottom and fixed temperature along the vertical sides. The instability threshold depends on the Prandtl number as well as the normalized flux difference ($f$) and decreases with the aspect ratio ($\epsilon$), following a $\epsilon f^{-1}$ power law. Using 3D initial value and 2D eigenvalue calculations, we identify a dominant 3D mode characterized by two transverse standing waves attached to the domain edges. We characterize the dominant mode's frequency and transverse wave number as functions of the Rayleigh number and aspect ratio. An analytical asymptotic solution for the base state in the bulk is obtained, valid over most of the domain and increasingly accurate for lower aspect ratios. A local stability analysis, based on the analytical base state, reveals oscillatory transverse instabilities consistent with the global instability characteristics. The source term for this most unstable mode appears to be interactions between vertical shear and horizontal temperature gradients.

physics.flu-dyn↗

arXiv2025

Experimental study of the convection in a thin cylindrical gas layer with imposed bottom and top fluxes and imposed side temperature

We investigate convection in a thin cylindrical gas layer with an imposed flux at the bottom and a fixed temperature along the side, using a combination of direct numerical simulations and laboratory experiments. The experimental approach allows us to extend by two orders of magnitude the explored range in terms of flux Rayleigh number. We identify a scaling law governing the root-mean-square horizontal velocity and explain it through a dimensional analysis based on heat transport in the turbulent regime. Using particle image velocimetry, we experimentally confirm, for the most turbulent regimes, the presence of a drifting persistent pattern consisting of radial branches, as identified by Rein et al. (2023, J. Fluid Mech. 977, A26). We characterise the angular drift frequency and azimuthal wavenumber of this pattern as functions of the Rayleigh number. The system exhibits a wide distribution of heat flux across various time scales, with the longest fluctuations attributed to the branch pattern and the shortest to turbulent fluctuations. Consequently, the branch pattern must be considered to better forecast important wall heat flux fluctuations, a result of great relevance in the context of nuclear safety, the initial motivation for our study.

physics.flu-dyn↗

arXiv2024

Internal shear layers generated by a vertically oscillating cylinder in unbounded and bounded rotating fluids

In rotating fluids, the viscous smoothing of inviscid singular inertial waves leads to the formation of internal shear layers. In previous works, we analysed the internal shear layers excited by a viscous forcing (longitudinal libration) in a spherical shell geometry (He \textit{et al.}, \textit{J. Fluid Mech.} {\bf 939}, A3, 2022; {\bf 974}, A3, 2023). We now consider the stronger inviscid forcing corresponding to the vertical oscillation of the inner boundary. We limit our analysis to two-dimensional geometries but examine three different configurations: freely-propagating wave beams in an unbounded domain and two wave patterns (a periodic orbit and an attractor) in a cylindrical shell geometry. The asymptotic structures of the internal shear layers are assumed to follow the similarity solution of Moore \& Saffman (\textit{Phil. Trans. R. Soc. Lond. A}, 264 (1156), 1969, 597-634) in the small viscous limit. The two undefined parameters of the similarity solution (singularity strength and amplitude) are derived by asymptotically matching the similarity solution with the inviscid solution. For each case, the derivation of the latter is achieved either through separation of variables combined with analytical continuation or the method of characteristics. Global inviscid solutions, when obtained, closely match numerical solutions for small Ekman numbers far from the critical lines, while viscous asymptotic solutions show excellent performance near those lines. The amplitude scalings of the internal shear layers excited by an inviscid forcing are found to be divergent as the Ekman number $E$ decreases, specifically $O(E^{-1/6})$ for the critical point singularity and $O(E^{-1/3})$ for attractors, in contrast to the convergent scalings found for a viscous forcing.

physics.flu-dyn↗

arXiv2024

Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection. The second one is driven by vertical heat transfers analogous to Rayleigh Benard convection. We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.

physics.flu-dyn↗

arXiv2024

Inertial wave super-attractor in a truncated elliptical cone

We consider inertial waves propagating in a fluid contained in a non-axisymmetric three-dimensional rotating cavity. We focus on the particular case of a fluid enclosed inside a truncated cone or frustum, which is the volume that lies between two horizontal parallel planes cutting an upright cone. While this geometry has been studied in the past, we generalise it by breaking its axisymmetry and consider the case of a truncated elliptical cone for which the horizontal sections are elliptical instead of circular. The problem is first tackled using ray tracing where local wave packets are geometrically propagated and reflected within the closed volume without attenuation. We complement these results with a local asymptotic analysis and numerical simulations of the original linear viscous problem. We show that the attractors, well-known in two dimensional or axisymmetric domains, can be trapped in a particular plane in three-dimension provided that the axisymmetry of the domain is broken. Contrary to previous examples of attractors in three-dimensional domains, all rays converge towards the same limit cycle regardless of initial conditions, and it is localised in the bulk of the fluid.

physics.flu-dyn↗

arXiv2023

Internal shear layers in librating spherical shells: the case of attractors

Following our previous work on periodic ray paths (He et al, 2022), we study asymptotically and numerically the structure of internal shear layers for very small Ekman numbers in a three-dimensional (3D) spherical shell and in a two-dimensional (2D) cylindrical annulus when the rays converge towards an attractor. We first show that the asymptotic solution obtained by propagating the self-similar solution generated at the critical latitude on the librating inner core describes the main features of the numerical solution. The internal shear layer structure and the scaling for its width and velocity amplitude in $E^{1/3}$ and $E^{1/12}$ respectively are recovered. The amplitude of the asymptotic solution is shown to decrease to $E^{1/6}$ when it reaches the attractor, as it is also observed numerically. However, some discrepancies are observed close to the particular attractors along which the phase of the wave beam remains constant. Another asymptotic solution close to those attractors is then constructed using the model of Ogilvie (2005). The solution obtained for the velocity has an $O(E^{1/6})$ amplitude, but a different self-similar structure than the critical-latitude solution. It also depends on the Ekman pumping at the contact points of the attractor with the boundaries. We demonstrate that it reproduces correctly the numerical solution. Surprisingly, the solution close to an attractor with phase shift (that is an attractor that touches the axis in 3D or in 2D with a symmetric forcing) is found to be much weaker.

physics.flu-dyn↗

arXiv2023

Suppression of wall modes in rapidly rotating Rayleigh-B\'enard convection by narrow horizontal fins

The heat transport by rapidly-rotating Rayleigh-B\'enard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes which develop along vertical walls, significantly perturbing the heat flux. We show that narrow horizontal fins along the vertical walls efficiently suppress wall modes ensuring that their contribution to the global heat flux is negligible compared with bulk convection in the geostrophic regime, thereby paving the way for new experimental studies of geophysically relevant regimes of rotating convection.

physics.flu-dyn↗

arXiv2023

Effects of particle size and background rotation on the settling of particle clouds

We experimentally investigate the behaviour of instantaneous localised releases of heavy particles falling as turbulent clouds in quiescent water, both with and without background rotation. We present the results of 514 systematic experiments for no rotation and for three rotation rates $\Omega = 5,10,20$rpm, and for the size of particles in the range $5\mu m$ to $1mm$, exploring four decades of the Rouse number $\mathcal{R} \in [6\times 10^{-4},4]$ which quantifies the inertia of particles. In the canonical framework of turbulent thermals described by Morton \textit{et al.}, [Proc. R. Soc. A: Math. Phys. Sci. \textbf{234}, 1 (1956)], we compare particle clouds with salt-water thermals to highlight specificities due to the particulate nature of the turbulence forcing. In the absence of rotation, particle clouds initially behave as salty thermals with a modulation of their entrainment capacity, which is optimally enhanced for a finite inertia $\mathcal{R}\simeq 0.3$ due to particulate effects. However this regime of turbulence is limited in time due to the inertial decoupling between turbulent eddies and particles. For the three values of $\Omega$ explored here, the particulate enhancement of entrainment is inhibited. Moreover the cloud's expansion is interrupted when the Coriolis force overcomes its inertia, forcing the cloud to transform into vortical columnar flows which considerably increase the residence time of particles.

physics.flu-dyn↗

arXiv2022

Zonal jets experiments in the gas giants' zonostrophic regime

Intense east-west winds called zonal jets are observed in the atmospheres of Jupiter and Saturn and extend in their deep interior. We present experimental results from a fully three-dimensional laboratory analog of deep gas giants zonal jets. We use a rapidly rotating deep cylindrical tank, filled with water, and forced by a small-scale hydraulic circulation at the bottom. A topographic $\beta$-effect is naturally present because of the curvature of the free surface. Instantaneous turbulent zonal jets spontaneously emerge from the small-scale forcing, equilibrate at large scale, and can contain up to 70% of the total kinetic energy of the flow once in a quasi-steady state. We show that the spectral properties of the experimental flows are consistent with the theoretical predictions in the zonostrophic turbulence regime, argued to be relevant to gas giants. This constitutes the first fully-experimental validation of the zonostrophic theory in a completely three-dimensional framework. Complementary, quasi-geostrophic (QG) simulations show that this result is not sensitive to the forcing scale. Next, we quantify the potential vorticity (PV) mixing. While PV staircasing should emerge in the asymptotic regime of the gas giants, only a moderate PV mixing occurs because of the strong forcing and dissipation, as confirmed by QG simulations at smaller Ekman number. We quantify the local PV mixing by measuring the equivalent of a Thorpe scale, and confirm that it can be used to estimate the upscale energy transfer rate of the flow, which otherwise needs to be estimated from a much more demanding spectral analysis.

physics.geo-ph↗

arXiv2022

Localized layers of turbulence in stratified horizontally sheared Poiseuille flow

This article presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds up on the previous work that originally detected the linear instability of such configuration, by means of experiments, theoretical analysis and numerical simulations \citep{G21}. We extend hereafter this former investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We notice that the flow loses its vertical homogeneity through a secondary bifurcation, due to harmonic resonances, and further describe this symmetry-breaking mechanism in the vicinity of the instability threshold. When departing away from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of horizontal localized layers of stratified turbulence surrounded by quiescent regions of meandering waves.

physics.flu-dyn↗

arXiv2022

Competition between Rayleigh--B\'enard and horizontal convection

We investigate the dynamics of a fluid layer subject to an imposed bottom heat flux and a top monotonically-increasing temperature profile driving horizontal convection. We use direct numerical simulations and consider a large range of flux-based Rayleigh numbers $10^6 \leq Ra_F \leq 10^9$ and imposed top horizontal to bottom vertical heat flux ratios $0 \leq \Lambda \leq 1$. The fluid domain is a closed two-dimensional box with aspect ratio $4\leq \Gamma \leq 16$ and we consider no-slip boundaries and adiabatic side walls. We demonstrate a regime transition from Rayleigh--B\'enard convection (RB) to horizontal convection (HC) at $\Lambda\approx 10^{-2}$, which is independent of $Ra_F$ and $\Gamma$. At small $\Lambda$, the flow is organized in multiple overturning cells with approximately unit aspect ratio, while at large $\Lambda$ a single cell is obtained. The RB-relevant Nusselt number scaling with $Ra_F$ and the HC-relevant Nusselt number scaling with the horizontal Rayleigh number $Ra_L=Ra_F\Lambda\Gamma^4$ are in good agreement with previous results from classical RB convection and HC studies in the limit $\Lambda \ll 10^{-2}$ and $\Lambda \gg 10^{-2}$, respectively. We demonstrate that the system is multi-stable near the transition $\Lambda\approx10^{-2}$, i.e. the exact number of cells not only depends on $\Lambda$ but also on the system's history. Our results suggest that subglacial lakes, which motivated this study, are likely to be dominated by RB convection, unless the slope of the ice-water interface, which controls the horizontal temperature gradient via the pressure-dependence of the freezing point, is greater than unity.

physics.flu-dyn↗

arXiv2022

Spontaneous suppression of inverse energy cascade in instability-driven 2D turbulence

Instabilities of fluid flows often generate turbulence. Using extensive direct numerical simulations, we study two-dimensional turbulence driven by a wavenumber-localised instability superposed on stochastic forcing, in contrast to previous studies of state-independent forcing. As the contribution of the instability forcing, measured by a parameter $\gamma$, increases, the system undergoes two transitions. For $\gamma$ below a first threshold, a regular large-scale vortex condensate forms. Above this threshold, shielded vortices (SVs) emerge within the condensate. At a second, larger value of $\gamma$, the condensate breaks down, and a gas of weakly interacting vortices with broken symmetry spontaneously emerges, characterised by preponderance of vortices of one sign only and suppressed inverse energy cascade. The latter transition is shown to depend on the damping mechanism. The number density of SVs in the broken symmetry state slowly increases via a random nucleation process. Bistability is observed between the condensate and mixed SV-condensate states. Our findings provide new evidence for a strong dependence of two-dimensional turbulence phenomenology on the forcing.

physics.flu-dyn↗

arXiv2021

Surfing on turbulence: a strategy for planktonic navigation

In marine plankton, many swimming species can perceive their environment with flow sensors. Can they use this flow information to travel faster in turbulence? To address this question, we consider plankters swimming at constant speed, whose goal is to move upwards. We propose a robust analytical behavior that allows plankters to choose a swimming direction according to the local flow gradients. We show numerically that such plankters can "surf" on turbulence and reach net vertical speeds up to twice their swimming speed. This new physics-based model suggests that planktonic organisms can exploit turbulence features for navigation.

physics.flu-dyn↗

arXiv2021

Surface Manifestation of Stochastically Excited Internal Gravity Waves

Recent photometric observations of massive stars show ubiquitous low-frequency "red-noise" variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. On the other hand, theoretical calculations by Shiode et al (2013) and Lecoanet et al (2019) predict IGWs should manifest at the surface as regularly-spaced peaks associated with standing g-modes. In this work, we compare these theoretical approaches to simplified 2D numerical simulations. The simulations show g-mode peaks at their surface, and are in good agreement with Lecoanet et al (2019). The amplitude estimates of Shiode et al (2013) did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we find good agreement with simulations. However, simulations need to be run for hundreds of convection turnover times for the peaks to become visible; this is a long time to run a simulation, but a short time in the life of a star. The final spectrum can be predicted by calculating the wave energy flux spectrum in much shorter simulations, and then either applying the theory of Shiode et al (2013) or Lecoanet et al (2019).

astro-ph.SR↗

arXiv2021

Spontaneous knotting of a flexible fiber in chaotic flows

We consider the problem of an inextensible but flexible fiber advected by a steady chaotic flow, and ask the simple question whether the fiber can spontaneously knot itself. Using a 1D Cosserat model, a simple local viscous drag model and discrete contact forces, we explore the probability of finding knots at any given time when the fiber is interacting with the ABC class of flows. The bending rigidity is shown to have a marginal effect compared to that of increasing the fiber length. Complex knots are formed up to 11 crossings, but some knots are more probable than others. The finite-time Lyapunov exponent of the flow is shown to have a positive effect on the knot probability. Finally, contact forces appear to be crucial since knotted configurations can remain stable for times much longer than the turnover time of the flow, something that is not observed when the fiber can freely cross itself.

cond-mat.soft↗