Abstract
The present paper deals with the stability problem of incompressible, inviscid and density stratified fluid in a channel with arbitrary cross section. For this problem we derive a criterion for long wave stability namely, if the wave number is less than or equal to a critical wave number \(k_{c}\) then the disturbances is stable. The result is illustrated with plane Poiseuille flow and Couette flow basic flows. Furthermore, we have obtained an upper bound for the growth rate of an unstable mode, which is sharper than the known ones. Moreover, a parabolic instability region which does not depend on any condition and which intersect the known semielliptical instability region is derived under some conditions.
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We are thankful to the referees for their comments and suggestions which helped us to improve the presentation of the paper.
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Priya, K.R., Ganesh, V. On the Criterion for Long Wave Stability of Shear Flows. Int. J. Appl. Comput. Math 4, 142 (2018). https://doi.org/10.1007/s40819-018-0581-z
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DOI: https://doi.org/10.1007/s40819-018-0581-z