Waves in the gas centrifuge: asymptotic theory and similarities with the atmosphere

Abstract

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration

“…Fruman (2009) computed the analytical solution for meridionally confined zonally propagating waves for the linearised hydrostatic Boussinesq equations including the full Coriolis terms. Studies involving non-traditional effects were also conducted by de Verdière & Schopp (1994), Maas & Harlander (2007), Igel & Biello (2020), Rodal & Schlutow (2021) and Perez, Delplace & Venaille (2022).…”

Instability of the isothermal, hydrostatic equatorial atmosphere at rest under the full Coriolis acceleration

“…Fruman [2009] computed the analytical solution for meridionallyconfined zonally-propagating waves for the linearised hydrostatic Boussinesq equations including the full Coriolis terms. Studies involving non-traditional effects were also conducted by Colin de Verdière and Schopp [1994], Maas and Harlander [2007], Rodal and Schlutow [2021].…”