A Possible Mechanism for Boundary Layer Mixing and Layer Formation in a Stratified Fluid

Abstract

A plate tilted at 42° from the horizontal is oscillated along its length with frequency ω and amplitude a in a linearly stratified fluid (salt water) of kinematic viscosity ν. If the Reynolds number Rc = a(ω/ν)½ is small, a parallel oscillating boundary layer is set up. As Re is increased from zero the parallel flow becomes unstable. If ω2≲N̂2 (where N̂ is a transverse Brunt-Väisälä frequency), the motion appears to be a convective overturning associated with periodic reversals of the density gradient. If ω2≪N̂2, these plumes just mix up the fluid next to the plate. If, however, ω2≈N̂2 and Re is not too large, then the plumes interact with the oscillating shear flow and mix in such a way as to set up layers which extend into the interior of the fluid. It is suggested that these effects might also be present when internal waves propagate over a slope.