# Jérémie Vidal's research while affiliated with Université Grenoble Alpes and other places

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## Publications (33)

Changes in the Earth’s rotation are deeply connected to fluid dynamical processes in the outer core. This connection can be explored by studying the associated Earth eigenmodes with periods ranging from nearly diurnal to multi-decadal. It is essential to understand how the rotational and fluid core eigenmodes mutually interact, as well as their dep...

The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093) pioneered a method to compu...

The acoustic modes of a rotating fluid-filled cavity can be used to determine the effective rotation rate of a fluid (since the resonant frequencies are modified by the flows). To be accurate, this method requires a prior knowledge of the acoustic modes in rotating fluids. Contrary to the Coriolis force, centrifugal gravity has received much less a...

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magneti...

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magneti...

The acoustic modes of a rotating fluid-filled cavity can be used to determine the effective rotation rate of a fluid (since the resonant frequencies are modified by the flows). To be accurate, this method requires a prior knowledge of the acoustic modes in rotating fluids. Contrary to the Coriolis force, centrifugal gravity has received much less a...

The generation of mean flows is a long-standing issue in rotating fluids. Motivated by planetary objects, we consider here a rapidly rotating fluid-filled spheroid, which is subject to weak perturbations of either the boundary (e.g. tides) or the rotation vector (e.g. in direction by precession, or in magnitude by longitudinal librations). Using bo...

The generation of mean flows is a long-standing issue in rotating fluids. Motivated by planetary objects, we consider here a rapidly rotating fluid-filled spheroid, which is subject to weak perturbations of either the boundary (e.g. tides) or the rotation vector (e.g. in direction by precession, or in magnitude by longitudinal librations). Using bo...

The acoustic spectrum of a gas-filled resonating cavity can be used to indirectly probe its internal velocity field. This unconventional velocimetry method is particularly interesting for opaque fluid or rapidly rotating flows, which cannot be imaged with standard methods. This requires to (i) identify a large enough number of acoustic modes, (ii)...

Convection in a spherical shell is widely used to model fluid layers of planets and stars. The choice of thermal boundary conditions in such models is not always straightforward. To understand the implications of this choice, we report on the effects of the thermal boundary condition on thermal convection, in terms of instability onset, fully devel...

Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency $|\omega_t|$ exceeds the turnover frequency $\omega_{c\nu}$ of the dominant con...

Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency $|\omega_t$ exceeds the turnover frequency $\omega_{cv}$ of the dominant convec...

The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093. doi:10.1098/rspa.2014.0093) pioneered a method to compu...

The acoustic spectrum of a gas-filled resonating cavity can be used to indirectly probe its internal velocity field. This unconventional velocimetry method is particularly interesting for opaque fluid or rapidly rotating flows, which cannot be imaged with standard methods. This requires to (i) identify a large enough number of acoustic modes, (ii)...

Compressible fluid modes in rigid ellipsoids: towards modal acoustic velocimetry - Volume 885 - Jérémie Vidal, Sylvie Su, David Cébron

Convection is thought to act as a turbulent viscosity in damping tidal flows and in driving spin and orbital evolution in close convective binary systems. This turbulent viscosity should be reduced, compared to mixing-length predictions, when the forcing (tidal) frequency $|\omega_t|$ exceeds the turnover frequency $\omega_{cv}$ of the dominant con...

Convection is thought to act as a turbulent viscosity in damping tidal flows and in driving spin and orbital evolution in close convective binary systems. This turbulent viscosity should be reduced, compared to mixing-length predictions, when the forcing (tidal) frequency $|{\omega}_t|$ exceeds the turnover frequency ${\omega}_{cv}$ of the dominant...

In planetary fluid cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection (DDC). We investigate rotating DDC (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compo...

Context. Surface magnetic fields have been detected in 5–10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interactio...

Surface magnetic fields have been detected in 5% to 10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, i.e. inherited from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS collaboration. Thus, different ph...

Celestial fluid bodies (e.g. planets, stars), orbited by gravitational companions, undergo harmonic orbital forcings, such as tides or precession. These orbital forcings deform fluid bodies into ellipsoids and generate fluid instabilities, e.g. the elliptical instability. The nonlinear outcome of these instabilities can sustain a wave turbulence re...

We consider the hydrodynamic stability of homogeneous, incompressible and rotating ellipsoidal fluid masses. The latter are the simplest models of fluid celestial bodies with internal rotation and subjected to tidal forces. The classical problem is the stability of Roche–Riemann ellipsoids moving on circular Kepler orbits. However, previous stabili...

Stellar magnetism plays an important role in stellar evolution theory. Approximatively 10% of observed main sequence (MS) and pre-main-sequence (PMS) radiative stars exhibit surface magnetic fields above the detection limit, raising the question of their origin. These stars host outer radiative envelopes, which are stably stratified. Therefore they...

[This corrects the article DOI: 10.1371/journal.pone.0178599.].

Magnetohydrodynamic (MHD) ships represent a clear demonstration of the Lorentz force in fluids, which explains the number of students practicals or exercises described on the web. However, the related literature is rather specific and no complete comparison between theory and typical small scale experiments is currently available. This work provide...

Discussion of electrolysis complications.
(ZIP)

Mean field of a cylindrical magnet.
(ZIP)

α and β for the Hartmann flow.
(ZIP)

Analytical solutions for the thruster.
(ZIP)

We investigate free hydromagnetic eigenmodes of an incompressible, inviscid and ideal electrically conducting fluid in rotating triaxial ellipsoids. The container rotates with an angular velocity tilted from its figure. The magnetic base state is a uniform current density also tilted. Three-dimensional perturbations upon the base state are expanded...

We investigate free hydromagnetic eigenmodes of an incompressible, inviscid and ideal electrically conducting fluid in rotating triaxial ellipsoids. The container rotates with an angular velocity tilted from its figure. The magnetic base state is a uniform current density also tilted. Three-dimensional perturbations upon the base state are expanded...

Seismic waves sensitive to the outermost part of the Earth's liquid core seem
to be affected by a stably stratified layer at the core-mantle boundary. Such a
layer could have an observable signature in both long-term and short-term
variations of the magnetic field of the Earth, which are used to probe the flow
at the top of the core. Indeed, with t...

## Citations

... Very small time steps must be taken due to the small period of the oscillations, and the proximity of various branches of solutions lengthens the transients. Despite the difficulties, the experimental and numerical studies have intensified in recent years, reaching low Ekman numbers at the very low Pr of liquid metals, E, [1][2][3][4], or taking into account new phenomena such us the precession of the rotating spheres [5], the compressibility of the fluid [6,7], the influence of Robin [8] and fixed-flux [9] boundary conditions for the temperature, or attaining the fully developed turbulence [10,11]. ...

... The Ekman number scalings we have observed are very different from the zonal flows generated by tidal forcing in a full sphere in the experiments (with a deformable no-slip boundary) of, for example, Morize et al. (2010), where the zonal velocity scales as 2 E −3/10 , or for those produced by libration-driven inertial waves, as studied in Cébron et al. (2021) and Lin & Noir (2021), where it instead scales as 2 E 0 or 2 E −1/10 , respectively (though these also result from self-interaction, so the zonal velocity also scales as 2 ). We underline that the best fitting laws here seem quite different from the ones emerging in Paper I in E −3/2 and E −1/2 , presumably because of (3, 3). ...

... Fully spectral algorithms that rely on global polynomial descriptions satisfying the boundary conditions have already proven accurate for this problem in spheres [35][36][37], but such methods remained to be devised for dynamos in ellipsoids. We thus develop here a fully spectral algorithm in triaxial ellipsoids, motivated by our previous hydrodynamic works in ellipsoids [38,39]. To sidestep the known difficulties of the ellipsoidal coordinate system, we employ the Cartesian coordinates and expand the magnetic field onto global Cartesian polynomial elements satisfying local boundary conditions (BC), namely pseudovacuum or perfectly conducting BC. ...

Reference: Kinematic dynamos in triaxial ellipsoids

... Orbital forcings (e.g., tides, precession or librations) can notably drive suitable large-scale oscillating flows in non-spherical planetary cores (e.g., Le Bars et al. 2015;Tilgner 2015), which typically vary on diurnal time scales in the inertial frame (see Fig. 3). Since convection varies on much longer time scales in the core (typically a few decades or even longer), turbulent convection is not expected to be efficient in damping these large-scale orbitally driven flows (Goodman and Oh 1997;Vidal and Barker 2020). Hence, these orbital flows with nearly diurnal frequencies certainly coexist with turbulent convection on very long time scales, and several pairs of inertial modes could be involved in (14) to trigger flow instabilities. ...

... It is known that a first-order perturbation treatment is generally inaccurate to predict the angular frequency of the acoustic modes in strongly flattened bodies [31,39]. Indeed, second-order corrections in 2 can become non-negligible when 10 −1 (e.g. for the upper branch in the top panel), which are realistic values for rapidly rotating planets (table 1) or experiments [64]. ...

... While some studies suggest that the physical mechanism responsible for the tidal dissipation is the turbulent cascade of energy from large to small scales (Zahn (1989); Zahn & Bouchet (1989); Goldreich & Keeley (1977); Penev et al. (2009)), other suggest the damping of internal waves inside the star (Goodman & Dickson (1998); Essick & Weinberg (2016); Ogilvie (2013); Rieutord & Valdettaro (2010)). With several flavors of each type of mechanism suggested, the exact dissipation mechanisms are still under debate, leading to inconsistencies among various models (Ogilvie & Lesur (2012); Vidal & Barker (2020); Preece et al. (2019)). The efficiency of the tidal dissipation has also been studied empirically, often parameterized as a dimensionless parameter: tidal quality factor Q = Q /k2 (Goldreich & Soter (1966)), where 1/Q is the energy lost over one tidal period normalized by the energy stored in the tidal deformation; k2 is the ratio between the linear perturbation of the self-gravitation potential ine-mail: rxp163130@utdallas.edu ...

... Fully spectral algorithms that rely on global polynomial descriptions satisfying the boundary conditions have already proven accurate for this problem in spheres [35][36][37], but such methods remained to be devised for dynamos in ellipsoids. We thus develop here a fully spectral algorithm in triaxial ellipsoids, motivated by our previous hydrodynamic works in ellipsoids [38,39]. To sidestep the known difficulties of the ellipsoidal coordinate system, we employ the Cartesian coordinates and expand the magnetic field onto global Cartesian polynomial elements satisfying local boundary conditions (BC), namely pseudovacuum or perfectly conducting BC. ...

Reference: Kinematic dynamos in triaxial ellipsoids

... Yet, a fast numerical algorithm is still lacking to accurately perform the ellipsoidal harmonic transformation, and so this approach has not been considered yet in any numerical models. Alternatively, fully spectral Galerkin descriptions based on global polynomials in the Cartesian coordinates have been developed to solve the diffusionless fluid modes in full ellipsoids (Vantieghem 2014;Vidal et al. 2019Gerick et al. 2020;. A wealth of intuition about the fluid modes in non-spherical geometries has built up using the latter approach, but it cannot be used for non-vanishing viscosity (to match the tangential BC of the velocity field), or in ellipsoidal shells. ...

... In DDC, the potential energy associated with the destabilising component is released through the rapid molecular diffusion of temperature (Stern, 1960), and the resulting vertical flows can significantly enhance the transport of heat and composition in stable layers . DDC has been extensively studied in oceanography (Schmitt, 1994;Kunze, 2003), magma chambers (Sparks et al., 1984;Hansen & Yuen, 1990) and astrophysics (Garaud, 2018), but has only been investigated by a few studies in the context of planetary cores Net et al., 2012;Bouffard et al., 2017;Monville et al., 2019;Silva et al., 2019;Mather & Simitev, 2021). Yet, if present, DDC would distort the magnetic field passing through the layer, thereby affecting the observable magnetic field. ...

... Indeed, the critical magnetic field for Tayler instability is reached here through some intermediate, weak kinematic dynamo triggered by the differential rotation, which we refer to as weak dynamos in the following. According to self-consistent numerical simulations, many candidates may play this role in stellar interiors (32,(36)(37)(38). ...

Reference: Hidden dynamo spins down radiative stars