By using characteristic analysis of the linear and nonlinear parabolic stability equations ( PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub- characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic., respectively . The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories , the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time , the methods of removing the remained ellipticity are further obtained from the nonlinear PSE .
Wave breaking statistics, such as the whitecap coverage and average volume of broken seawater, are evaluated in terms of wave parameters by use of wave breaking model (Yuan et al., 1988) taking the fifth order Stokes's wave as the analog of the original wave field. Based on the observed fact that breaking waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean, the influence of wave breaking on air-sea fluxes of heat and moisture is investigated. Theoretical expressions of bubble-volume flux and sea spray spectrum at the sea surface and models for bubble-induced and spray droplet-induced heat and moisture fluxes are established. This work can be taken as the basis for further understanding the mechanism of air-sea coupling and parameterization models.
