The hydrodynamic stability of a one-dimensional transient buoyancy-induced flow

Abstract Recent experiments have shown that a transient, buoyant, laminar and one-dimensional flow adjacent to a vertical flat surface may become vigorous enough to begin a transition process from laminar to turbulent flow. The disturbance amplification characteristics of such a flow are analyzed using linear stability theory. The Orr-Sommerfeld equations for stream function and temperature disturbances are formulated for an imposed constant and uniform base surface heat flux. These equations are solved for water, Pr = 6.7, with a step in surface heat flux from zero to a non-zero value. The temporal amplification of the disturbance components is found as a function of their frequency. The results are plotted on a stability plane which shows that the selective amplification found in steady, downstream-developing buoyancy driven flows also occurs in transients. The new results are shown to be in moderate agreement with recent measurements. Temperature and velocity disturbance profiles across the boundary region are also examined. For the same boundary conditions, the qualitative effect of Pr on the temporal growth of disturbances is also discussed.