Abstract
Many naturally-occurring and man-made phenomena can cause mixing in a stably-stratified environment, and thus result in the formation of mixed fluid regions. In the ocean, for example, turbulent mixing can be caused by tidal flow over bottom topography, by breaking internal waves or by a submarine traveling through the oceanic thermocline. Since the mixed fluid region has excess potential energy over its surroundings, the fluid must move towards a new stable equilibrium state; this results in the collapse of the mixed region. The character of this collapse is generally complicated and depends on various parameters including the shape and dimensions of the mixed region, the channel depth and the background stratification profile. The collapse of an axisymmetric mixed region in a continuously stratified pycnocline is analyzed using direct simulation of the Navier-Stokes equations in the Boussinesq limit. Attention is focused on cylindrical 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. The vortex roll-up is related to the strain-induced intensification of vorticity and is found to be most pronounced for ``tall'' and horizontally compact mixed regions. The wave and vortex gradually decay as they spread radially in the pycnocline. After significant decay has occurred, 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 particle scheme is used to visualize and quantify the wave structure. Analysis of particle distributions shows that the toroidal vortices entrain ambient stratified fluid into their cores. It is found that the speed of the cylindrical solitary wave is lower than the two-dimensional (2D) weakly-nonlinear prediction. In addition, unlike the 2D case, the wave speed does not appear to be a simple function of the wave amplitude. The vortex decay is finally analyzed in terms of a simplified model on the viscous cancellation of the two strained vortices of opposite sign. An approximate qualitative agreement between model predictions and computations is found. The comparison highlights the role of viscous diffusion of vorticity as well as the contributions of entrainment and baroclinic vorticity generation to the vortex decay.