A new instability driven by the combined effect of wind stress and rotation in a sheared liquid layer

TL;DR

This paper uncovers a new longwave instability mode in shear flows caused by the combined effects of wind stress and Earth's rotation, advancing understanding of oceanic flow dynamics.

Contribution

It introduces a novel instability mode driven by wind stress and rotation, supported by spectral and asymptotic analysis, revealing new insights into ocean flow behavior.

Findings

Identification of new longwave instability modes

Most unstable mode is a longwave spanwise disturbance

Asymptotic analysis confirms numerical results

Abstract

We examine the linear stability of a shear flow driven by wind stress at the free surface and rotation at the lower boundary, mimicking oceanic flows influenced by surface winds and rotation of Earth. The linearised eigenvalue problem is solved using the Chebyshev spectral collocation method and a longwave asymptotic analysis. Our results reveal new longwave instability modes that emerge for non-zero rotational Reynolds numbers. It is observed that the most unstable mode, characterised by the lowest critical parameters, corresponds to longwave spanwise disturbances with vanishing streamwise wavenumber. The asymptotic analysis, which shows excellent agreement with numerical results, analytically confirms the existence of this instability. Thus, the present study demonstrates the hitherto unreported combined influence of wind stress and rotation of Earth on ocean dynamics.