NUMERICAL STUDY OF HYDRODYNAMICS USING THE NONLINEAR SCHRODINGER-EQUATION

The hydrodynamical behavior of the nonlinear Schrodinger equation is investigated by Fourier pseudo-spectral direct numerical simulations. Its dispersive and nonlinear acoustics are characterized quantitatively and an equation that describes this regime at leading order is derived. A technique that allows the preparation of periodic initial data containing an arbitrary system of point vortices with minimal acoustic excitations is given. The Eulerian dynamics of a jet made of an array of counter rotating vortices is obtained. Sinuous and varicose instabilities are shown to take place. Finally the numerical methods best suited to study vortex-sound interactions are discussed.