# Experimental study of convection in the compressible regime

## TL;DR

This study experimentally investigates convection in a compressible fluid under high rotation, revealing a quasi-geostrophic flow regime, a classical heat flux scaling, and possible hysteresis effects influenced by compressibility and Coriolis forces.

## Contribution

First experimental analysis of compressible convection in a high-rotation regime with detailed flow characterization and hysteresis observations.

## Key findings

- Flow is in a quasi-geostrophic regime.
- A classical power law relates Nusselt and Rayleigh numbers.
- Hysteresis observed between high and low heat flux regimes.

## Abstract

An experiment of thermal convection with significant compressible effects is presented. The high-gravity environment of a centrifuge and the choice of xenon gas enable us to observe an average adiabatic temperature gradient up to 3.5 K cm$^{-1}$ over a 4 cm high cavity. At the highest rotation rate investigated, 9990 rpm, the superadiabatic temperature difference applied to the gas layer is less than the adiabatic temperature difference. The convective regime is characterized by a large Rayleigh number, about 10$^{12}$, and dominant Coriolis forces (Ekman number of order 10$^{-6}$). The analysis of temperature and pressure fluctuations in our experiments shows that the dynamics of the flow is in a quasi-geostrophic regime. Still, a classical power law (exponent 0.3 $\pm$ 0.04) is observed between the Nusselt number (dimensionless heat flux) and the superadiabatic Rayleigh number (dimensionless superadiabatic temperature difference). However, a potential hysteresis is seen between this classical high flux regime and a lower heat flux regime. It is unclear whether this is due to compressible or Coriolis effects. In the transient regime of convection from an isothermal state, we observe a local decrease of temperature which can only be explained by adiabatic decompression.