Fluid dynamics of a mixed convective/stably stratified system—A review of some recent works

Bars, Michaël Le; Couston, Louis-Alexandre; Favier, Benjamin; Léard, Pierre; Lecoanet, Daniel; Gal, Patrice Le

doi:10.5802/crphys.17

Cited by 3 publications

(1 citation statement)

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“…Buffett and Knezek (2018) investigated linear excitation and found that Maxwell stresses yield an efficient generation mechanism with most power in the period range 30 to 100 years, long compared to the timescales discussed here. We may learn also from other fluid systems where a stratified layer is adjacent to a turbulent layer such as the Earth's stratosphere or the Sun's tachocline (Le Bars et al 2020). The quasi-biennial oscillation of the Earth's atmosphere has been much studied.…”

Section: Mac Waves In a Stratified Layermentioning

confidence: 99%

A Dynamical Prospective on Interannual Geomagnetic Field Changes

2021

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Geomagnetic observations from satellites have highlighted interannual variations in the rate of change of the magnetic field originating from Earth's core. Downward continued to the core surface, these variations primarily show up in the equatorial belt. First, we recall the main characteristics of these patterns, addressing their spatio-temporal resolution, as seen from field models. We then review the several dynamical frameworks proposed so far to understand and model these observations, which populate the frequency spectrum on time scales close to the Alfvén time A ≈ 2 yr, much shorter than the vortex turnover time U ≈ 150 yr in Earth's core. Magnetic-Archimedes-Coriolis (MAC) waves in a stratified layer below the core surface constitute a first possibility in the case of a sub-adiabatic heat flux at the top of the core. Their period may reach the interannual range for a layer thickness less than ≈ 30 km, for a buoyancy frequency of the order of the Earth's rotation rate. An alternative has been proposed in a context where the Coriolis force dominates the momentum balance, rendering transient motions almost invariant along the rotation axis (quasi-geostrophy, QG). Torsional Alfvén waves, consisting of axisymmetric QG motions, operate at periods similar to the Alfvén time, but are not sufficient to explain the interannual field changes, which require non-axisymmetric motions. QG Alfvén waves (involving the Coriolis and magnetic forces) constitute another possibility, with inertia playing an important role. They have been detected in the latest generation of geodynamo simulations, propagating in a ubiquitous manner at a speed slightly less than the Alfvén velocity. They are localized in longitude and as a result their description requires high azimuthal wavenumber. But the branch of QG waves with large extent in azimuth is also worth considering, as it reaches interannual periods as their radial wavenumber is increased. The excitation of such high-frequency dynamics is discussed with respect to the temporal spectrum of the core field, which presents a slope ∼ f −4 for periods approximately between A and U . We finally summarize the main geophysical implications of the existence of this interannual dynamics on core and lower mantle structure, properties, and dynamics.

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Section: Mac Waves In a Stratified Layermentioning

confidence: 99%

A Dynamical Prospective on Interannual Geomagnetic Field Changes

2021

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Single-Mode Solutions for Convection and Double-Diffusive Convection in Porous Media

Liu

Knobloch

2022

Fluids

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This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal.

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