Boundary layers due to shear flow over a still fluid: A direct integration approach

摘要

The flow of a shear-driven upper fluid above an otherwise still fluid is considered. This two-fluid problem is transformed into two sets of ordinary differential equations coupled only at the interface. The two sets of ODEs are integrated simultaneously by means of a double-shooting technique for some different parameter values. The new direct integration approach may readily enable extensions to non-Newtonian rheology. The present formulation shows beyond any doubt that the density ratio and the viscosity ratio between the two fluids are the two controlling parameters. The similarity solutions revealed that the asymmetric mixing region extends far deeper into the lower fluid then upwards into the streaming shear flow.