Study on Kelvin Helmholtz shear flows subjected to differential rotation

TL;DR

This study investigates how the Coriolis force, due to differential rotation, suppresses Kelvin-Helmholtz instability in shear flows, revealing similarities to magnetic field effects and showing increased vortex formation under rotation.

Contribution

It demonstrates the suppression of KHI by the Coriolis force and draws an analogy between rotational effects and magnetic fields in shear flow dynamics.

Findings

Coriolis force suppresses long-wavelength KHI modes

Rotation leads to more vortices compared to non-rotating flows

Qualitative agreement between numerical and analytical results

Abstract

A numerical simulation of Kelvin-Helmholtz Instability (KHI) in parallel shear flows subjected to external rotation is carried out using a pseudo-spectral technique. The Coriolis force, arising in a rotation frame under the beta plane approximation, tends to suppress the growth of KHI modes. The numerical results show a close qualitative agreement with the analytical results obtained for a step-wise shear flow profile. Experimental evidence demonstrates that particles in a rotating frame experience the Coriolis force, mathematically equivalent to the Lorentz force. Therefore, the Coriolis force affects fluid dynamics in a manner similar to the Lorentz force in magnetized shear flows. This paper exploits the analogy between the magnetic field and rotation to study effects equivalent to a magnetic field on KHI in a rotating frame. Similar to the magnetic field case, the Coriolis force suppresses KHI and tends to form compressed and elongated KH vortex structures. However, the magnetic field and Coriolis force act on different scales, with the latter suppressing long-wavelength mode perturbations. A higher number of vortices are observed in the presence of rotation compared to non-rotating cases