Abstract
A weakly nonlinear analysis of the downstream evolution of weakly unstable disturbances
in a stably stratified mixing layer with a large Reynolds number is carried out.
No other requirements are imposed upon velocity and density profiles, thus making
it possible to overcome the restrictions placed in earlier studies (Brown & Stewartson
1978; Brown et al. 1981; Churilov & Shukhman 1987, 1988) by a particular choice
of weakly supercritical flow models assuming symmetry. For each of the two critical
layer regimes possible here, viscous and unsteady, evolution equations are obtained,
their solutions and competition between nonlinearities in the course of instability
development are analysed, and evolution scenarios for unstable disturbances are constructed
for different levels of their supercriticality. It is established that the regime
with a nonlinear critical layer does not arise in an evolutionary manner, except for
the previously studied case of a weak stratification (Shukhman & Churilov 1997). It
is shown that while in the viscous critical layer regime the relaxation of assumptions
of the symmetry and weak supercriticality of the flow produces no fundamental
changes in the theory, in the unsteady critical layer regime a new (non-dissipative
cubic) nonlinearity appears which governs the instability development on equal terms
with two already known nonlinearities. Results are illustrated by calculations for two
families of flow models with a controlled degree of asymmetry.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
4 articles.
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