K. Fujimura and R.E. Kelly: Interaction between longitudinal convection rolls and transverse waves in unstably stratified plane Poiseuille flow, Phys. Fluids 7 (1995) 68-79.

Abstract

Nonlinear interaction between a Tollmien-Schlichting wave and longitudinal rolls resulting from Rayleigh-Benard instability has been investigated in an unstably stratified plane Poiseuille flow of infinite extent. Cubic order amplitude equations for the interacting modes are derived on a weakly nonlinear basis in the neighborhood of a crossover point at which both modes become unstable on a linear basis simultaneously. A bifurcation analysis based on use of the actual numerical coefficients obtained from the governing equations and evaluated for various values of the Prandtl number is performed, and the results, such as the effect of longitudinal rolls on the subcritical instability characteristic of a Tollmien-Schlichting wave, are discussed.

H.S. Li and K. Fujimura, Nonlinear critical Reynolds number of a stratified plane Poiseuille flow, Phys. Fluids 8 (1996) 1127-1129.

Abstract

The minimum Reynolds number, Re_c^N, below which all the two-dimensional and monochromatic wave disturbances decay, is studied numerically for a thermally stratified plane Poiseuille flow. The Re_c^N is found to be sensitive to the change of Prandtl number P. Under unstable stratification with Rayleigh number just below critical, Re_c^N=1000 is found for P<10^-3.

Related paper

K. Fujimura and R.E. Kelly: Stability of unstably stratified shear flow between parallel plates, Fluid Dynamics Research 2 (1988) 281-292.