We consider classical shallow-water equations for a rapidly rotating fluid layer, f_o 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 equationscan be Decomposed an U(t,x_1, x_2) =U(t, x_1,x_2)+W'(t,x_1x_2)+r where U 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/(F_0μ) where μ is the Lebesgue measure of almost resonant Aspect rations.
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