Abstract
Abstract
Highlights
Kelvin–Helmholtz instability (KHI) is believed to be important in geophysical flows found in both the oceans (Smyth & Moum 2012) and atmosphere (Fukao et al 2011; Sun et al 2015)
This paper presents a systematic study of the nonlinear behaviour of the Drazin model of a two-dimensional finite Reynolds number stratified shear layer – a hyperbolic tangent shear and constant density gradient – at three different values of Pr, using both the tracking of exact coherent structures in the forced system and direct numerical simulation (DNS) of the forced and unforced systems
In the Pr = 0.7 case, we found a simple, supercritical pitchfork bifurcation, with the resulting steady-state Kelvin–Helmholtz billows increasing in amplitude as Richardson number is decreased, so far as we could track them
Summary
Kelvin–Helmholtz instability (KHI) is believed to be important in geophysical flows found in both the oceans (Smyth & Moum 2012) and atmosphere (Fukao et al 2011; Sun et al 2015). The two most commonly used, the Drazin (1958) and Holmboe (unpublished lecture notes 1960) models, are both found to be linearly stable in the inviscid case when the minimum gradient Richardson number Rim (as defined below) is greater than one quarter. We argue for the former scenario by presenting direct evidence that two-dimensional finite-amplitude billow-like states exist for Rim 0.4 – i.e. substantially above 1/4 – for Pr 2.3 and indirect evidence that this situation continues below this threshold. This implies that complicated temporal dynamics is possible for flows generally considered inert due to a lack of a Kelvin–Helmholtz linear instability.
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