ANZIAM J.
43 (2002), 409427

Nonlinear evolution of singular disturbances to a
tanh^{3} y mixing layer

S. Saujani
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada


J. Drozd
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada


and

R. Mallier
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada



Abstract

We consider the nonlinear evolution of a
disturbance to a mixing layer, with the base
profile given by
u_{0}(y) = tanh^{3} y
rather than the more usual tanh y,
so that the first two derivatives of u_{0}
vanish at y = 0.
This flow admits three neutral modes, each of
which is singular at the critical layer. Using
a nonequilibrium 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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