ANZIAM J.
43 (2002), 409-427
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Nonlinear evolution of singular disturbances to a
tanh3 y mixing layer
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S. Saujani
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada
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J. Drozd
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada
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and
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R. Mallier
Department of Applied Mathematics
University of Western Ontario
London ON N6A 5B7
Canada
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Abstract
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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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