Stratified Kolmogorov flow. (Q2777872)

The authors have investigated the Kolmogorov flow (a shear flow with a sinusoidal velocity profile) in a weekly stratified, two-dimensional flow. The amplitude equation for the system has been derived in a neigbourhood of the initial bifurcation to instability for both low and high Péclet numbers. The amplitude equation has been solved numerically, and it has been found that, for low Péclet number, the stratification stops the cascade of energy from small to large scales at an intermediate wave number. For high Péclet number, in diffusively spreading thermal boundary layers the stratification temporarily impedes the growth of instability. The instability eventually mixes the temperature inside the boundary layers, so releasing itself from the stabilizing stratification, and thereby grows more quickly. The governing fluid equations have been solved numerically, and the solutions are compared with the results obtained by asymptotic analysis.