Numerical study of wave-mean flow and wave-wave interactions in linearly stratified fluids

Wave-mean flow and wave-wave interactions play essential roles in the ocean and atmosphere; they are dynamic processes that govern the energy transport and energy spectral distribution. The wave-mean flow interactions investigated here are critical layer processes while the wave-wave interactions are triad resonant interactions. They are investigated through numerical simulation and stability analysis.;It is shown that Rayleigh-Taylor instability in the spanwise direction is the most unstable mode involved in breakdown at critical level. On the second issue, single and multiple triad interactions are studied. If resonance is maintained at small scales, the energy transfer becomes weak due to triad geometry. The energy transfer to small scale modes can be significant due to nonlinearity; the behavior is non-resonant but may be explosive. To explore the role of resonant interactions in the ocean, a Garrett-Munk oceanic energy spectrum is used as the initial condition for numerical simulations, and the bispectrum and phase correlation analyses are used to search for resonant triads. Resonant interactions occur only at very large scales and are of the local sum resonance type. Parametric subharmonic instabilities are insignificant in energy transfer. At small scales, wave-mean flow interactions dominate.;Three issues are addressed. First, what is the instability that initiates wave breakdown in critical layer processes? Second, can the energy of a primary wave be transferred directly to very small scales? Third, what is the role of resonant interactions in the deep ocean?...