arXiv subjects

Alban Pothérat

Publications and source records attributed to Alban Pothérat.

At least 19 recordsLinked to original sources

arXiv2026

Regimes of rotating convection in an experimental model of the Earth's tangent cylinder

Earth's fast rotation imposes the Taylor-Proudman Constraint that opposes fluid motion across an imaginary cylindrical surface called the Tangent Cylinder (TC) obtained by extruding the equatorial perimeter of the solid inner core along the rotation direction, and up to the core-mantle boundary (CMB). To date, however, the influence of this boundary is unknown, and this impedes our understanding of the flow in the polar regions of the core. We reproduce the TC geometry experimentally, where the CMB is modelled as a cold, cylindrical vessel, with a hot cylinder inside it acting as the inner solid core. The vessel is filled with water to optically map the velocity field in regimes of criticality and rotational constraint consistent with those of the Earth. We find that the main new mechanism arises out of the inertia near the cold lateral boundary of the vessel, which drives inertia at the outer boundary of the TC, as convection in the equatorial regions of the Earth's core does. The baroclinicity just outside the TC suppresses the classical wall modes found inside a solid cylinder, and the inertia there causes an early breakup of the TPC at the TC boundary. The flow remains dominated by the Coriolis force even up to criticality of 191, but because of inertia near the TC boundary, geostrophic turbulence appears at much lower criticality than in other settings. The heat flux escapes increasingly through the TC boundary as the TPC becomes weaker. Hence, inertia driven by baroclinicity outside the TC provides a convenient shortcut to geostrophic turbulence, which is otherwise difficult to reach in experiments. These results also highlight a process whereby the convection outside the TC may control turbulence inside it and bypass the axial heat transfer. We finally discuss how Earth's conditions, especially its magnetic field, may change how this process acts within the Earth's core.

physics.geo-ph↗

arXiv2025

Phenomenology of laminar acoustic streaming jets

This work identifies the physical mechanisms at play in the different flow regions along an Eckart acoustic streaming jet by means of numerical simulation based on a novel modeling of the driving acoustic force including attenuation effects. The flow is forced by an axisymmetric beam of progressive sound waves attenuating over a significant part of a closed cylindrical vessel where the jet is confined. We focus on the steady, axisymmetric and laminar regime. The jet typically displays a strong acceleration close to the source before reaching a peak velocity. At further distances from the transducer, the on-axis jet velocity smoothly decays before reaching the opposite wall. For each of these flow regions along the jet, we derive scaling laws for the on-axis velocity with the magnitude of the acoustic force and the diffraction of the driving acoustic beam. These laws highlight the different flow regimes along the jet and establish a clear picture of its spatial structure, able to inform the design of experimental or industrial setups involving Eckart streaming jets.

physics.flu-dyn↗

arXiv2025

Suppressing instabilities in mixed baroclinic flow using an actuation based on receptivity

This paper presents a method to stabilise oscillations occurring in a mixed convective flow in a nearly hemispherical cavity, using actuation based on the receptivity map of the unstable mode. This configuration models the continuous casting of metallic alloys, where hot liquid metal is poured at the top of a hot sump with cold walls pulled in a solid phase at the bottom. The model focuses on the underlying fundamental thermo-hydrodynamic processes without dealing with the complexity inherent to the real configuration (Flood & Davidson 1994). This flow exhibits three branches of instability (Kumar & Poth{é}rat 2020). The solution of the adjoint eigenvalue problem for the convective flow equations reveals that the regions of highest receptivity for unstable modes of each branch concentrate near the inflow upper surface. Simulations of the linearised governing equations show that a thermo-mechanical actuation modelled on the adjoint eigenmode asymptotically suppresses the unstable mode. If the actuation's amplitude is kept constant in time, which is easier to implement in an industrial environment, the suppression is still effective but only over a finite time, after which it becomes destabilising. Based on this phenomenology, we apply the same actuation during the stabilising phase only in the nonlinear evolution of the unstable mode. It turns out stabilisation persists, even when the unstable mode is left to evolve freely after the actuation period. These results not only demonstrate the effectiveness of receptivity-informed actuation in stabilising convective oscillations but also suggest a simple strategy for their long-term control.

physics.flu-dyn↗

arXiv2025

Stability of acoustic streaming jets

We study the stability of a steady Eckart streaming jet that is acoustically forced at one end of a closed cylindrical cavity and impinges the wall at the other end, where a recirculation forms. This configuration generically represents industrial processes where acoustic forcing offers a contactless means of stirring or controlling confined flows. Successfully doing so, however, requires sufficient insight into the topology of the acoustically forced flow. This raises the question of whether the base acoustic streaming jet is stable and, when not, of which alternative states emerge. Using Linear Stability Analysis (LSA) and three-dimensional nonlinear simulations, we identify the instability mechanisms and determine the nature of the bifurcations that ensue. We show that the ratio $C_R$ between the cavity and the maximum beam radii determines the dominant unstable mode. For $4 \leq C_R \leq 6$, a non-oscillatory perturbation rooted in the jet impingement triggers a supercritical bifurcation. For $C_R = 3$, the flow destabilises through a subcritical non-oscillatory bifurcation. Further reducing $C_R$ increases the shear within the flow, and gradually relocates the instability in the shear layer between impingement-induced vortices: for $C_R = 2$, an unstable travelling wave grows out of a subcritical bifurcation, which becomes supercritical for $C_R=1$. For each geometry, the nonlinear 3D simulations validate the LSA, identify the saturated nonlinear state and its stability. This study offers fundamental insight into the stability of acoustically-driven flows in general, but also opens possible pathways to either induce turbulence acoustically, or to avoid it in realistic configurations.

physics.flu-dyn↗

arXiv2025

Seven decades of exploring planetary interiors with rotating convection experiments

The interiors of many planets consist mostly of fluid layers. When these layers are subject to superadiabatic temperature or compositional gradients, turbulent convection transports heat and momentum. In addition, planets are fast rotators. Thus, the key process that underpins planetary evolution, the dynamo action, flow patterns and more, is rotating convection. Because planetary interiors are inaccessible to direct observation, experiments offer physically consistent models that are crucial to guide our understanding. If we can fully understand the laboratory model, we may eventually fully understand the original. Experimentally reproducing rotating thermal convection relevant to planetary interiors comes with specific challenges, e.g. modelling the central gravity field of a planet that is parallel to the temperature gradient. Three classes of experiments tackle this challenge. One approach consists of using an alternative central force field, such as the electric force. These are, however, weaker than gravity and require going to space. Another method entails rotating the device fast enough so that the centrifugal force supersedes Earth's gravity. This mimics the equatorial regions of a planet. Lastly, by using the actual lab gravity aligned with the rotation axis, insight into the polar regions is gained. These experiments have been continuously refined during the past seven decades. We review their evolution, from the early days of visualising the onset patterns of convection, over central force field experiments in spacecrafts, liquid metal experiments, to the latest optical velocity mapping of rotating magnetoconvection in sulfuric acid inside high-field magnets. We show how innovative experimental design and emerging experimental techniques advanced our understanding and painted a more realistic picture of planetary interiors, including Earth's liquid metal outer core.

physics.geo-ph↗

arXiv2025

Pulsatility delays the transition to sustained turbulence in quasi-two-dimensional shear flows

This work investigates efficient routes to turbulence in quasi-two-dimensional shear flows. Two-dimensional disturbances require high Reynolds numbers to incite transition from a steady base flow, as transient growth is modest. With the addition of an oscillatory base flow component, this work shows that the transient growth experienced by two-dimensional initial perturbations is often well above that provided by the steady component. However, as has been shown for three-dimensional flows [Pier & Schmid J. Fluid Mech. 926, A11 (2021)], the transient growth is almost entirely composed of modal intracyclic growth, rather than a transient mechanism which takes advantage of non-normality. This lack of transient growth, relative to the severe decay induced by the favorable pressure gradient during the acceleration phase of the oscillatory base flow, only ever delays the transition to sustained turbulence. Thus, a non-oscillatory driving force remains the most efficient strategy for sustained turbulence in quasi-two-dimensional shear flows. The only benefit provided by pulsatility is that the amplitude of the initial condition required to trigger intermittent turbulence is orders of magnitude smaller.

physics.flu-dyn↗

arXiv2025

Alfvén waves at low magnetic Reynolds number: Transitions between diffusion, dispersive Alfvén waves and nonlinear propagation

This paper seeks whether Alfvén waves (AW) can be produced in laboratory-scale liquid metal experiments, \emph{i.e.} at low-magnetic Reynolds Number ($R\!m$). AW are incompressible waves propagating along magnetic fields typically found geo and astrophysical systems. Until now, only faint linear waves have been experimentally produced in liquid metals because of the large magnetic dissipation they undergo when $R\!m\ll1$. Yet, controlling laboratory AW could emulate such far remote processes as anomalous heating in the solar corona, oscillations of the Earth inner core or turbulence in the solar wind. To answer this question, we force AW with an AC electric current in a liquid metal channel in a transverse magnetic field. We derive a wave-bearing extension of the usual low$-R\!m$ MHD approximation to identify two linear regimes: The purely diffusive regime exists when $N_ω$, the ratio of the oscillation period to the timescale of diffusive two-dimensionalisation by the Lorentz force, is small. The propagative regime is governed by the ratio of the forcing period to the AW propagation timescale which, we call the Jameson number $J\!a$ after Jameson (1964), JFM. In this regime, AW are dissipative and dispersive as they propagate more slowly where velocity gradients are higher. Both regimes are recovered in the FLOWCUBE experiment, in excellent agreement with the model up to $J\!a \lesssim 0.85$ but near the $J\!a=1$ resonance, high amplitude waves become clearly nonlinear. Hence, in electrically driving AW, we were able to produce some of the propagative, diffusive and nonlinear processes of astro and geophysical AW.

physics.flu-dyn↗

arXiv2024

Magnetic Taylor-Proudman constraint explains the flows into the Tangent Cylinder

Tangent Cylinders (TCs) have shaped our understanding of planetary dynamos and liquid cores. The Taylor-Proudman Constraint (TPC) due to planetary rotation creates these imaginary surfaces separating polar and equatorial regions but cannot explain the flows meandering through them. Here we establish and verify experimentally that magnetic fields aligned with rotation drive flows \emph{into} TCs, linked to the flows \emph{along} TCs by a \emph{magnetic} Taylor-Proudman constraint. This constraint explains and quantifies how magnetic fields reshape rotating flows in planetary interiors and magnetorotating flows in general.

physics.flu-dyn↗

arXiv2023

Subcritical transition to turbulence in quasi-two-dimensional shear flows

The transition to turbulence in conduits is among the longest-standing problems in fluid mechanics. Challenges in producing or saving energy hinge on understanding promotion or suppression of turbulence. While a global picture based on an intrinsically 3D subcritical mechanism is emerging for 3D turbulence, subcritical turbulence is yet to even be observed when flows approach two dimensions, e.g. under intense rotation or magnetic fields. Here, stability analysis and direct numerical simulations demonstrate a subcritical quasi-2D transition from laminar flow to turbulence, via a radically different 2D mechanism to the 3D case, driven by nonlinear Tollmien--Schlichting waves. This alternative scenario calls for a new line of thought on the transition to turbulence and should inspire new strategies to control transition in rotating devices and nuclear fusion reactor blankets.

physics.flu-dyn↗

arXiv2021

Stability of pulsatile quasi-two-dimensional duct flows under a transverse magnetic field

This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/53075Se8O0b1b109b1cc0061b280aaa122f0f92dc. The stability of a pulsatile quasi-two-dimensional duct flow was numerically investigated. Flow was driven, in concert, by a constant pressure gradient and by the synchronous oscillation of the lateral walls. This prototypical setup serves to aid understanding of unsteady magnetohydrodynamic flows in liquid metal coolant ducts subjected to transverse magnetic fields, motivated by the conditions expected in magnetic confinement fusion reactors. A wide range of wall oscillation frequencies and amplitudes were simulated. Focus was placed on the driving pulsation optimized for the greatest reduction in the critical Reynolds number, for a range of friction parameters $H$ (proportional to magnetic field strength). An almost $70$% reduction in the critical Reynolds number, relative to that for the steady base flow, was obtained toward the hydrodynamic limit ($H=10^{-7}$), while just over a $90$% reduction was obtained by $H=10$. For all oscillation amplitudes, increasing $H$ consistently led to an increasing percentage reduction in the critical Reynolds number. This is a promising result, given fusion relevant conditions of $H \geq 10^4$. These reductions were obtained by selecting a frequency that both ensures prominent inflection points, and a growth in perturbation energy in phase with deceleration of the base flow. Nonlinear simulations at the optimized frequency and amplitude still satisfied the no net growth condition at the greatly reduced critical Reynolds numbers. However, although the linear mode undergoes a symmetry breaking process, turbulence was not triggered. Nonlinear base flow modulation also arrested the linear decay of the perturbation, with exponential growth not observed at supercritical Reynolds numbers.

physics.flu-dyn↗

arXiv2021

Direct numerical simulation of quasi-two-dimensional MHD turbulent shear flows

Direct numerical simulations (DNS) are performed to study the turbulent shear flow of an electrically conducting fluid in a cylindrical container. The flow is driven by the interaction between the radial electric currents ($I$) injected through a large number of small electrodes at the bottom wall and an axial magnetic field. All the numerical parameters, including the geometry of the container, the total injcected currents and the magnetic field, are in line with the experiment performed in J. Fluid Mech. 456, 137-159. First, witth laminar Hartmann layers, three dimensional simulations recover experimentally measured quantities (global angular momentum, velocity profiles). The variation laws for the wall shear stresses, the energy spectra and visualizations of flow structures near the side wall highlight separation and turbulence within the side wall layers. Furthermore, a parametric analysis of the flow reveals that Ekman recirculations have significant influence on the vortex size, the free shear layer, and the global dissipation. Second, we recover the scaling laws of the cutoff scale that separate the large quasi-two-dimensional scales from the small three-dimensional ones (J. Fluid Mech. 118, 507-518), and thus establish their validity in sheared MHD turbulence. Furthermore, we find that three-componentality are and the three-dimensionality appear concurrently and that both the two-dimensional cutoff frequency and the mean energy associated to the axial component of velocity scale with $N_t$, respectively as $0.063N_t^{0.37}$ and $0.126 N_t^{-0.92}$.

physics.flu-dyn↗

arXiv2020

Transition to turbulence in quasi-two-dimensional MHD flow driven by lateral walls

This manuscript has been accepted for publication in Physical Review Fluids, see https://journals.aps.org/prfluids/accepted/d5074S28J6b11905012b7cb06505e8f2149dd5f20. This work investigates the mechanisms that underlie transitions to turbulence in a three-dimensional domain in which the variation of flow quantities in the out-of-plane direction is much weaker than any in-plane variation. This is achieved using a model for the quasi-two-dimensional magnetohydrodynamic flow in a duct with moving lateral walls and an orthogonal magnetic field. In this environment, conventional subcritical routes to turbulence, which are highly three-dimensional, are prohibited. To elucidate the remaining mechanisms involved in quasi-two-dimensional turbulent transitions, the magnetic field strength and degree of antisymmetry in the base flow are varied, the latter via the relative motion of the lateral duct walls. Introduction of any amount of antisymmetry to the base flow drives the critical Reynolds number infinite, as the TS instabilities take on opposite signs of rotation, and destructively interfere. However, an increasing magnetic field strength limits interaction between the instabilities, permitting finite critical Reynolds numbers. The transient growth only mildly depends on the base flow, with negligible differences for friction parameters $H \gtrsim 30$. Direct numerical simulations, initiated with random noise, indicate that for $H \leq 1$, supercritical exponential growth leads to saturation, but not turbulence. For higher $3 \leq H \leq 10$, a turbulent transition occurs, and is maintained at $H=10$. For $H \geq 30$, the turbulent transition still occurs, but is short lived, as the turbulent state quickly collapses. In addition, for $H \geq 3$, an inertial subrange is identified, with the perturbation energy exhibiting a $-5/3$ power law dependence on wave number.

physics.flu-dyn↗

arXiv2020

Subcritical route to turbulence via the Orr mechanism in a quasi-two-dimensional boundary layer

The link to the online abstract of this manuscript, accepted in Phys. Rev. Fluids, is https://journals.aps.org/prfluids/accepted/32074S4aH8b1c608e19768b42571f9001086a3f44. A subcritical route to turbulence via purely quasi-two-dimensional mechanisms, for a quasi-two-dimensional system composed of an isolated exponential boundary layer, is numerically investigated. Exponential boundary layers are highly stable, and are expected to form on the walls of liquid metal coolant ducts within magnetic confinement fusion reactors. Subcritical transitions were detected only at weakly subcritical Reynolds numbers (at most $\approx 70$% below critical). Furthermore, the likelihood of transition was very sensitive to both the perturbation structure and initial energy. Only the quasi-two-dimensional Tollmien-Schlichting wave disturbance, attained by either linear or nonlinear optimisation, was able to initiate the transition process, by means of the Orr mechanism. The lower initial energy bound sufficient to trigger transition was found to be independent of the domain length. However, longer domains were able to increase the upper energy bound, via the merging of repetitions of the Tollmien-Schlichting wave. This broadens the range of initial energies able to exhibit transitional behaviour. Although the eventual relaminarization of all turbulent states was observed, this was also greatly delayed in longer domains. The maximum nonlinear gains achieved were orders of magnitude larger than the maximum linear gains (with the same initial perturbations), regardless if the initial energy was above or below the lower energy bound. Nonlinearity provided a second stage of energy growth by an arching of the conventional Tollmien-Schlichting wave structure. A streamwise independent structure, able to efficiently store perturbation energy, also formed.

physics.flu-dyn↗

arXiv2020

PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow

We present the first simultaneous mapping of two-dimensional, time-dependent velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field. While electromagnetic forces are strongest in fluids of high electric conductivity such as liquid metals, their opacity excludes optical optical measurement methods. We circumvent this difficulty using a transparent electrolyte (Sulfuric acid), whose weaker conductivity is offset by higher magnetic fields. We describe an experimental rig based on this idea, where the Couette flow is entrained by a tape immersed in sulfuric acid and positioned flush onto the bore of large superconducting magnet, so that most of the flow is pervaded by a sufficiently homogeneous transverse magnetic field. Velocity and pressure fields are obtained by means of a bespoke PIV system, capable of recording the fluid's acceleration as well as its velocity. Both fields are then fed into a finite difference solver that extracts the pressure field from the magnetohydrodynamic governing equations. This method constitutes the first implementation of the pressure PIV technique to an MHD flow. Thanks to it, we obtain the first experimental velocity and pressure profiles in an MHD Couette flows and show that the transitional regime between laminar and turbulent states is dominated by near-wall, isolated, anisotropic perturbations.

physics.flu-dyn↗

arXiv2020

An effective two-dimensional model for MHD flows with transverse magnetic field

This paper presents a model for quasi two-dimensional MHD flows between two planes with small magnetic Reynolds number and constant transverse magnetic field orthogonal to the planes. A method is presented that allows to take 3D effects into account in a 2D equation of motion thanks to a model for the transverse velocity profile. The latter is obtained by using a double perturbation asymptotic development both in the core flow and in the Hartmann layers arising along the planes. A new model is thus built that describes inertial effects in these two regions. Two separate classes of phenomena are thus pointed out : the one related to inertial effects in the Hartmann layer gives a model for recirculating flows and the other introduces the possibility of having a transverse dependence of the velocity profile in the core flow. The ''recirculating'' velocity profile is then introduced in the transversally averaged equation of motion in order to provide an effective 2D equation of motion. Analytical solutions of this model are obtained for two experimental configurations : isolated vortices aroused by a point electrode and axisymmetric parallel layers occurring in the MATUR (MAgneticTURbulence) experiment. The theory is found to give a satisfactory agreement with the experiment so that it can be concluded that recirculating flows are actually responsible for both vortices core spreading and excessive dissipative behavior of the axisymmetric side wall layers.

physics.flu-dyn↗

arXiv2020

2D models for MHD flows

A new model is proposed for low $Rm$ MHD flows which remain turbulent even in the presence of a magnetic field. These flows minimize the Joule dissipation because of their tendency to become two-dimensional and, therefore to suppress all induction effects. However, some small three-dimensional effects, due to inertia and to the electric coupling between the core flow and the Hartmann layers, are present even within the core flow. This new model, which may be seen as an improvement of the Sommeria-Moreau 2D model, introduces this three-dimensionality as a small perturbation. It yields an equation for the average velocity over the magnetic field lines, whose solution agrees well with available measurements performed on isolated vortices.

physics.flu-dyn↗

arXiv2020

Numerical simulations of an effective two-dimensional model for flows with a transverse magnetic field

This paper presents simulations of the 2d model developed by Pothérat at al (\emph{J. Fluid Mech}, 2000) for MHD flows between two planes with a strong transverse homogeneous and steady magnetic field, accounting for moderate inertial effects in Hartmann layers. We first show analytically how the additional terms in the equations of motion accounting for inertia, soften velocity gradients in the horizontal plane, and then we implement the model on a code to carry out numerical simulations to be compared with available experimental results. This comparison shows that the new model can give very accurate results as long as the Hartmann layer remains laminar. Both experimental velocity profiles and global angular momentum measurements are closely recovered, and local and global Ekman recirculations are shown to alter significantly the aspect of the flow as well as the global dissipation.

physics.flu-dyn↗

arXiv2020

Low MHD turbulence: the role of boundaries

In this short review, we present the main known features of MHD Turbulence at Low Magnetic Reynolds number, for which the flow isn't intense nor electrically conductive enough to disturb an externally applied magnetic field. The emphasis is deliberately placed on the very specific physical mechanisms of these flows, rather than their numerical modelling. We also focus on homogeneous magnetic fields which have received most attention. Since the basic properties of these flows have been thoroughly reviewed a number of times, this review is deliberately biased towards flows in bounded domains, in which the tendency to two-dimensionality observed in MHD flows casts the boundaries of the domain into a leading role.

physics.flu-dyn↗