On Neutral and Unstable Modes and on the Role of Reynolds Stress in the Stability Problem of Density Stratified Shear Flows in Channels with Variable Bottom

Reddy, V R K and Subbiah, M (2019) On Neutral and Unstable Modes and on the Role of Reynolds Stress in the Stability Problem of Density Stratified Shear Flows in Channels with Variable Bottom. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 89 (4). pp. 777-790. ISSN 0369-8203

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Abstract

The stability problem of inviscid incompressible stratified shear flows in sea straits of arbitrary cross sections is formulated without the Boussinesq approximation. Series solutions of the stability equation are found by the method of Frobenius and these solutions are used to study the existence of neutral modes when the Richardson number is larger than one quarter. The energy aspect of the problem is studied by discussing the role of the Reynolds stress and its variation in the vertical direction for both unstable modes and neutral modes adjacent to the unstable modes. The interfacial conditions at layers of discontinuity of the basic velocity, density or topography are derived and these are used in the study of instability of two examples of basic flows.

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