The role of waves on mixing in shallow waters

Abstract

The role of waves on mixing is examined in a transverse shear flow in shallow waters for sub-critical, trans-critical, and super-critical flow over a range of convective Froude numbers. At low convective Froude numbers, the rollup of the vortex sheet to form an eddy defines the mixing. The mixing at higher convective Froude numbers, on the other hand, is affected by the shock waves and the radiation of the wave energy from an elongated vorticity element. Significant structural changes of the shear flow occur as the shock waves become discernible in the trans-critical and super-critical range of the convective Froude number. The shear layer growth is restrained while the momentum-thickness to vorticity-thickness ratio increases by a factor greater than 3. The fractional growth rate of the mixing layer in shallow waters and its dependence on the convective Froude number follows analogously the observed Mach-number dependence in gas dynamics.