Shape and size of large-scale vortices: A generic fluid pattern in geophysical fluid dynamics

Abstract

Planetary rotation organizes fluid motions into coherent, long-lived swirls, known as large-scale vortices (LSVs), which play an important role in the dynamics and long-term evolution of geophysical and astrophysical fluids. Here, using direct numerical simulations, we show that LSVs in rapidly rotating mixed convective and stably stratified fluids, which approximates the two-layer, turbulent-stratified dynamics of many geophysical and astrophysical fluids, have a generic shape and that their size can be predicted. We show that LSVs emerge in the convection zone from upscale energy transfers and can penetrate into the stratified layer. At the convective-stratified interface, the LSV cores have a positive buoyancy anomaly. Due to the thermal wind constraint, this buoyancy anomaly leads to winds in the stratified layer that decay over a characteristic vertical length scale. Thus LSVs take the shape of a depth-invariant cylinder with a finite-size radius in the turbulent layer and of a penetrating half dome in the stratified layer. Importantly, we demonstrate that when LSVs penetrate all the way through the stratified layer and reach a boundary that is no-slip, they saturate by boundary friction. We provide a prediction for the penetration depth and maximum radius of LSVs as a function of the LSV vorticity, the stratified layer depth, and the stratification. Our results, which apply for cyclonic LSVs, suggest that LSVs in slowly rotating stars and Earth's liquid core are confined to the convective layer, while in Earth's atmosphere and oceans they can penetrate far into the stratified layer.

Oscillatory thermal–inertial flows in liquid metal rotating convection

“…The occurrence of an inverse cascade is favoured by a two-dimensionality of the large-scale flow field (Kraichnan 1967;Boffetta & Ecke 2012), which can arise in geo-and astrophysical systems through the action of stabilizing forces such as the Coriolis force due to rotation or via Lorentz forces induced by magnetic fields. In rotating convection, LSV structures can form if there is sufficient turbulence in the flow field and Ro 1 so that the system-scale flow is quasi-two-dimensional (Favier, Silvers & Proctor 2014;Guervilly, Hughes & Jones 2014;Rubio et al 2014;Stellmach et al 2014;Couston et al 2020). Although our data are suggestive of a domain filling LSV, the limited radial coverage of the chord-probe data, u c (r > 0.7R), does not allow us to validate the existence of such a structure.…”

“…2014; Couston et al. 2020). Although our data are suggestive of a domain filling LSV, the limited radial coverage of the chord-probe data, , does not allow us to validate the existence of such a structure.…”

Rotation suppresses giant-scale solar convection

“…We anticipate at least an order of magnitude reduction. Specifically, an inverse cascade should transfer energy to barotropic differential rotation, not to larger convective motions (80,(98)(99)(100)(101)(102).…”

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

“…with an equivalent Prandtl number of 700, which seems at odds with our previous conclusion. Then from a numerical point of view, main challenges are: (i) to obtain QBO-like reversals in 3D direct numerical simulations of the full coupled system, and (ii) to extend our results on wave excitation and propagation to more realistic configurations, including in particular compressibility and rotation effects [39], as well as a spherical geometry. Finally, beyond atmospheric and stellar applications, it would be of great interest to evaluate the consequences of waves in other natural two-layer systems, like e.g.…”