Evolution and breaking of a propagating internal wave in stratified ocean

The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI (parametric subharmonic instability) involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE (kinetic energy) and PE (potential energy). The results show that the PE spectra display a wavenumber range scaling as 0.2N⁴k_y^-3 (N is the Brunt-Väisälä frequency, k_y is the vertical wavenumber), which is called buoyancy subrange. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.