The Onset and Nonlinear Development of Vortex Instabilities in a Horizontal Forced Convection Boundary Layer With Uniform Surface Suction

We consider the flow and heat transfer caused by a strong external flow passing over a hot surface with uniform surface suction. When the Péclet number based on the external velocity is sufficiently large, the resulting thermal boundary layer develops in a nonsimilar manner until it attains an asymptotic state which is independent of the streamwise coordinate, x, when it is dominated by the surface suction. For sufficiently large, but moderate, values of the Darcy–Rayleigh number this boundary layer becomes unstable to streamwise vortex disturbances. We employ a parabolic solver to determine how such disturbances, when placed very close to the leading edge, evolve with distance downstream. Neutral stability is then defined to be when a suitable energy functional ceases to decay/grow as x increases. Thus a neutral curve may be mapped out based upon the behaviour of this functional. Given that the uniform asymptotic state is well known to admit subcritical instabilities, our linearised analysis is extended into the nonlinear domain and the effect of different magnitudes of disturbance is ascertained. It is found that a surprisingly rich variety of vortex pattern emerges which is sometimes sensitively dependent on the values of the governing parameters. These patterns include wavy vortices and abrupt changes in perceived wavelength.