Dynamics and scale analysis of the transient convective flow induced by cooling a Pr

Abstract

The convective boundary layer flow as well as the subsequent intrusion flow induced by cooling an initially isothermal and quiescent fluid at Pr<1 using a linear thermal forcing is investigated with a scaling analysis in the present study. It is demonstrated that the thickness of the convective boundary layer flow does not depend on the streamwise position in both the initial growth and the fully developed states, whilst the characteristic velocity is constantly streamwise location-dependant in these two states. It is also shown that the oscillatory behaviour of flow parameters in the transitional state of the boundary layer flow is dramatically weaker than the classical homogenously thermal forcing problems. Four possible flow regimes are identified for the cold intrusion flow and it is revealed that their occurrence is unconditional, which dramatically differentiates from the flow associated with Pr>1 fluids. It is further found that the first flow regime, i.e. the unsteady viscous-buoyancy dominance, is ephemeral in nature and can therefore be ignored. The intrusion flow can thus be practically divided into three flow regimes: an unsteady inertia-buoyancy regime; a steady inertia-buoyancy regime; and a steady viscous-buoyancy flow regime. The scaling relations quantifying the convective flow in different flow states are obtained. Selected scales are validated against the DNS (Direct Numerical Simulation) results and a good agreement is achieved.