Three-dimensional inviscid waves in buoyant boundary layer flows

Abstract

The stability of weakly three-dimensional buoyancy-driven boundary layers to travelling waves is considered. It is shown that in the absence of cross ow inviscid modes are unstable and, as the degree of cross ow is increased, the short waves are the ÿrst to be stabilised -longer waves require an enhanced level of three-dimensionality of the basic ow for stabilisation. A combination of asymptotic and numerical techniques are used to provide a complete description of the inviscid modes over the whole wavenumber spectrum. The study is also extended to consider pure vortex "roll-cell" modes which can exist within unstably stratiÿed (buoyancy driven) ows and these are found to stabilise in the presence of cross ow.

The Nonparallel Evolution of Nonlinear Short Waves in Buoyant Boundary Layers

“…where the similarity variable η =Ỹ x (m−1)/2 , provided the far-field flow is u e (x) = x m and the wall temperature T w (x) = x (5m−1)/2 . The functions f, g, and q are given by the solution of a sixth-order system of differential equations (see [22] for details). A typical form of the streamwise flow is illustrated in Figure 1; here m = 1/3 and corresponds to the flow past a swept right-angled wedge.…”

The trailing-edge problem for mixed-convection flow past a horizontal plate

“…A forward integration has been done by Steinrück (2001) and Lagree (2001). However, regarding stability, interesting phenomena occur which have been investigated by Denier, Stott & Bassom (2001).…”