NUMERICAL STUDY OF THE COLLAPSE OF AN AXISYMMETRICAL MIXED REGION IN A PYCNOCLINE

The collapse of an axisymmetric mixed region in a continuously stratif ied pycnocline is analyzed using direct simulation of the Navier-Stoke s equations in the Boussinesq limit. Attention is focused on cylindric al mixed regions of size comparable to the thickness of the pycnocline , which lies between two deep layers of different densities. Computed results show that the collapse leads to the formation of a cylindrical internal gravity wave that encloses a concentrated toroidal vortex. T he vortex roll-up is related to the strain-induced intensification of vorticity and is found to be most pronounced for ''tall'' and horizont ally compact mixed regions. The wave and vortex gradually decay as the y spread radially in the pycnocline. After significant decay has occur red, the vortex disintegrates but the wave continues to propagate away from the mixed region. A sharp-nosed intrusion is left in the wake of the wave, which is no longer able to transport fluid. A Lagrangian pa rticle scheme is used to visualize and quantify the wave structure. An alysis of particle distributions shows that the toroidal vortices entr ain ambient stratified fluid into their cores. It is found that the sp eed of the cylindrical solitary wave is lower than the two-dimensional (2D) weakly-nonlinear prediction. In addition, unlike the 2D case, th e wave speed does not appear to be a simple function of the wave ampli tude. The vortex decay is finally analyzed in terms of a simplified mo del on the viscous cancellation of the two strained vortices of opposi te sign. An approximate qualitative agreement between model prediction s and computations is found. The comparison highlights the role of vis cous diffusion of vorticity as well as the contributions of entrainmen t and baroclinic vorticity generation to the vortex decay. (C) 1998 Am erican Institute of Physics.