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The influence of shear on double-diffusive and settling-driven instabilities

Abstract : The effects of shear on double-diffusive fingering and on the settling-driven instability are assessed by means of a transient growth analysis. Employing Kelvin waves within a linearized framework allows for the consideration of time-dependent waveforms in uniform shear. In this way, the effects of boundaries and of shear-driven instability modes can be eliminated, so that the influence of shear on the double-diffusive and settling-driven instabilities can be analyzed in isolation. Shear is seen to dampen both instabilities, which is consistent with previous findings by other authors. The shear damping is more pronounced for parameter values that produce larger unsheared growth. These trends can be explained in terms of instantaneous linear stability results for the unsheared case. For both double-diffusive and settling-driven instabilities, low P r-values result in less damping and an increased importance of the Orr mechanism, for which a quantitative scaling law is obtained.
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N. Konopliv, Lutz Lesshafft, E. Meiburg. The influence of shear on double-diffusive and settling-driven instabilities. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 849, pp.902-926. ⟨10.1017/jfm.2018.432⟩. ⟨hal-02322685⟩

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