Study of vortex breakdown in a stratified fluid

An analysis shows that nonsmooth solutions have to be considered. Weak solutions to the Euler equations describing an incompressible stratified fluid under gravity are defined and studied. The study makes use of a wave energy functional proposed for the nonlinear equations. It is shown that the Euler equations are insufficient for stating a well-posed generalized problem. Additional conditions based on physical considerations are proposed. One condition is energy conservation, and the other is a constraint imposed on the density, which is required for stability. A numerical method is developed that is used to analyze how wave breakdown in a stratified fluid depends on stratification. The numerical results are in satisfactory agreement with experiments.