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

TL;DR

This paper demonstrates that a gas centrifuge can serve as a laboratory model for Earth's atmosphere, exhibiting similar internal wave behaviors and dispersion relations, enabling experimental studies of atmospheric internal waves.

Contribution

It introduces an asymptotic theoretical framework showing the similarity between internal waves in a gas centrifuge and the atmosphere, highlighting experimental feasibility.

Findings

Internal waves in centrifuge match atmospheric dispersion relations

Optimal rotational frequency around 10,000 rpm for air

Lower heat capacity gases reduce required rotational speeds

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 circa 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 rounds per minute. Using gases of lower heat capacities at constant pressure, like 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.