Abstract:
A one-dimensional evolutionary system of equations is proposed, which describes in the Boussinesq approximation the motion of a thin bottom layer in a flooded domain of a lighter fluid, taking into account the development of shear instability and the formation of an intermediate mixing layer. For hydrostatic flows, the propagation velocities of perturbations are determined, and the concept of subcritical (supercritical) flow is formulated. The stationary problem of the mixing layer is considered. It is shown that, depending on the Froude number of the incoming flow, either a monotonic or a wave-type mixing layer is formed. In the first case, a regime of maximum entrainment is achieved, and the stationary solution is determined over a finite interval. When accounting for non-hydrostatic pressure in the lower layer, stationary solutions are constructed in the form of second-mode solitary waves adjacent to a given steady flow. Unsteady calculations of the formation and propagation of large-amplitude bottom waves were performed.
Fulltext:
PDF file (452 kB)
First page:
PDF file