The Boussinesq approximation in rapidly rotating flows

TL;DR

This paper introduces a modified Boussinesq approximation that includes centrifugal buoyancy effects, which are typically neglected but are important in rapidly rotating astrophysical and geophysical flows, improving modeling accuracy.

Contribution

The authors develop a new Boussinesq-type approximation that consistently incorporates centrifugal effects, addressing a gap in modeling rapidly rotating flows.

Findings

The new approximation captures centrifugal buoyancy effects neglected in traditional models.

Numerical comparisons show the new approach improves accuracy in rotating flow simulations.

Application to accretion disks demonstrates relevance to astrophysical phenomena.

Abstract

In commonly used formulations of the Boussinesq approximation centrifugal buoyancy effects related to differential rotation, as well as strong vortices in the flow, are neglected. However, these may play an important role in rapidly rotating flows, such as in astrophysical and geophysical applications, and also in turbulent convection. We here provide a straightforward approach resulting in a Boussinesq-type approximation that consistently accounts for centrifugal effects. Its application to the accretion-disk problem is discussed. We numerically compare the new approach to the typical one in fluid flows confined between two differentially heated and rotating cylinders. The results justify the need of using the proposed approximation in rapidly rotating flows.