We consider classical shallow-water equations for a rapidly rotating fluid layer, f0 being the Coriolis parameter with periodic or no-flux boundary conditions. The Poincare/Kelvin linear propagator describes fast oscillating waves for the linearized system. Solutions of the full nonlinear shallow-water equations can be decomposed as U(t, x1, x2) = Ū(t, x1, x2)+W′(t, x1, x2)+r where Ū is a solution of the quasigeostrophic equation. We show that the remainder r is uniformly (in initial data and spatial periods which are not resonant) estimated from above by a majorant of order 1/(f0μ) where μ is the Lebesgue measure of almost resonant aspect ratios. The existence on a long time interval T* of regular solutions to classical shallow-water equations with general initial data and aspects ratio (T*→+∞, as 1/f0→0) is proven. The vector field W′(t, x1, x2) describes the rapidly oscillating ageostrophic component with phase-locked turbulence. This component is exactly solved (for generic aspect ratios and symmetric initial data equivalent to no-flux boundary conditions) in terms of Poincare-Kelvin waves with phase shifts explicitly determined from the nonlinear quasigeostrophic equations.
|Original language||English (US)|
|Number of pages||30|
|Journal||European Journal of Mechanics, B/Fluids|
|State||Published - Jan 1 1997|
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)