Unsteady vortex pattern in a flow over a flat plate at zero angle of attack (two-dimensional problem)

Abstract

A technique of self-consistent analytical and numerical modeling of strongly and weakly (with the buoyancy frequency N = 1.2 and 0.02 s⁻¹) stratified flows, as well as of almost and absolutely homogeneous flows (with N = 10⁻⁵ and 0.0 s⁻¹), is developed using the fundamental system of equations without additional hypotheses or constants. Using an open-source software, the basic physical parameters (velocity, density, pressure) and their derivatives in the flow around a thick (0.5 cm) and a relatively thin (0.05 cm) rectangular plate 10 cm long are first calculated within the framework of a unique formulation over a wide range of velocities 0 < U < 80 cm/s. A complex flow structure comprising leading disturbances, internal waves, vortices, and thin interlayers is visualized. The maximal gradients are observed near the leading edge. In the unsteady vortex regime the structural parameters vary due to the nonlinear interaction of the flow components with different scales. For the finite plate, the calculated friction differs substantially from the Blasius solution but, for a semi-infinite plate, agrees to the accuracy of 5%.