We consider classical Boussinesq equations for a rotating stably stratified fluid with large N0 = N/F, where N0 describes the stratification, Ω0 = NΩ is the rate of rotation, and N is a large scaling parameter. Solutions of full nonlinear Boussinesq equations have a decomposition of the form U(t, x1, x2, x3) = Ũ(t, x1, x2, x3) + Wg(t, x1, x2, x3) + r, where Ũ is a solution of the quasigeostrophic equation and r is a remainder, which is uniformly bounded above by a majorant of the order of 1/N. The vector field Wg(t, x1, x2, x3) describes the rapidly oscillating gravity wave component The "amplitude" of this component describes the propagation of slow waves, and it satisfies a linear equation with coefficients determined by the quasigeostrophic component found from the nonlinear quasigeostrophic equations. The control of the error r based on estimates related to small denominators, for generic values of parameters, is used to prove the existence, on a long time interval T*, of regular solutions to classical Boussinesq equations with general initial data (T* → + ∞ as N → ∞).
|Original language||English (US)|
|Number of pages||12|
|Journal||Russian Journal of Mathematical Physics|
|State||Published - Dec 1 1996|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics