Effects of buoyancy on the lower branch modes on a Blasius boundary layer
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Date
2007-10
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Publisher
Journal of Discrete and Continuous Dynamical Systems series B
Abstract
The effect of thermal buoyancy on the stability properties of lower
branch Tollmein–Schlichting waves are investigated. At moderate values of
thermal buoyancy the standard triple deck structure, which describes the evo-
lution of such short wavelength instabilities in a buoyant boundary layer, is
unaltered. The leading order eigenrelation is now a function of thermal buoy-
ancy and from it we can derive the new dominant length- and time–scales for
the instability in the case when the boundary layer is strongly buoyant. These
new scales demonstrate that, in the case of strong wall cooling the lower branch
structure is identical to the upper branch structure, thus suggesting that the
curve of neutral stability may become closed at some large value of a Reynolds
number. In the alternate limit of strong wall heating the evolution of a fixed
frequency disturbance is governed by the linearized interactive boundary-layer
equations; in this case wave–like disturbances cannot be described by any form
of the quasi–parallel approximation theory.
Description
Keywords
Lower branch; thermal buoyancy; Tollmein-Schlichting waves; eigenrelation