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Nonlinear evolution of singular disturbances to a tanh3 y mixing layer

Publisher： Cambridge University Press

E-ISSN： 1446-8735|43|3|409-427

ISSN： 1446-1811

Source： ANZIAM Journal, Vol.43, Iss.3, 2002-01, pp. : 409-427

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Abstract

We consider the nonlinear evolution of a disturbance to a mixing layer, with the base profile given by u0(y) = tanh3 y rather than the more usual tanh y, so that the first two derivatives of u0 vanish at y = 0. This flow admits three neutral modes, each of which is singular at the critical layer. Using a non-equilibrium nonlinear critical layer analysis, equations governing the evolution of the disturbance are derived and discussed. We find that the disturbance cannot exist on a linear basis, but that nonlinear effects inside the critical layer do permit the disturbance to exist. We also present results of a direct numerical simulation of this flow and briefly discuss the connection between the theory and the simulation.

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