Vortex dynamics on Rotating Penetrative Convection

This work presents experimental results regarding rotating penetrative convection. The focus is on how convection driven by thermal or salty composition interacts with a stably stratified region. In such systems, as convection overshoots into the stratified layer, complex feedback loops arise, leading to the generation of internal waves that propagate in the stably stratified region. In rotating systems, Coriolis effects can further modify the dynamics, giving rise to inertial-gravity waves in the stably stratified region. Furthermore, the convective cells can change into different patterns of elongated vortices, changing how convection overshoots, and how it can drive internal waves. These phenomena are relevant to different geophysical and astrophysical applications, such as in the Earth's atmosphere, where internal gravity waves are excited in the stratosphere by convective motions in the troposphere. These interactions are also relevant to planetary and stellar interior applications, where convection can drive waves in stably stratified layers such as the radiative zone of stars or in the (possibly existing) stratified layer at the Earth's external core, where rotation effects are even more significant due to the small Rossby numbers, of the order of $10^{-5}$ to $10^{-4}$. This indicates that rotational forces dominate over inertial forces, highlighting the importance of better understanding the effects of rotation in the dynamics of penetrative convection and wave interactions.

Our experimental setup, named \textit{CROISSANTS (Convective ROtational Interactions with Stable Stratification Arising Naturally in Thermal Systems)}, found at the Physics Laboratory of the Ecole Normale Supérieure (ENS) de Lyon, is mounted on a rotating table and investigates the dynamics of rotating systems using water with a temperature gradient. The temperature ranges from approximately $30^oC$ at the top of a $30$cm-high cubic cavity and decreases to $0^oC$ at the bottom. Since water exhibits a density inversion between $0^oC$ and $4^oC$, the system naturally develops convection at the bottom, beneath a stably stratified region that extends from the convective interface to the top of the cavity. Measurements were performed using techniques such as Particle Image Velocimetry (PIV), Schlieren techniques, and Laser-Induced Fluorescence (LIF), to capture the convective and wave motions in both vertical and horizontal planes. Numerical simulations complement the experiments, exhibiting similar behavior to the observed experimental results. Both experiments and numerical simulations show that the elongated vortices in the convective region can be observed in higher regions of the stable density stratified zone. These long-lasting vortices move slowly in the flow (compared to the rotation of the experiment). Lagrangian-Averaged-Vorticity-Deviation (LAVD) techniques are then applied to track the dynamics of these long-lasting vortices elongated in the stable region. Understanding these processes provides a framework for interpreting how convective motion transfers energy across scales, impacting large-scale magnetic fields and planetary evolution.