By Derome J., Zhang D.L.

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**Additional info for A short course on atmospheric and oceanic waves**

**Sample text**

Averaging over a wave period, T, gives A2 ⎛kω + β/2⎞

Recall that in our previous model, the Coriolis parameter, f, was treated as a constant, namely, the earth curvature has been neglected. This assumption is valid only when the application range of latitude is small. In this chapter we shall show that if we allow f to vary with latitude when it is differentiated, we will find a type of low-frequency (ω < f) waves, called Rossby waves, that are of most importance for large-scale flows. Rossby waves exist in either a stratified fluid or a homogenous layer of fluid.

The scale at which the earth rotation becomes as important as gravity in determining the frequency of surface gravity waves is obtained by setting f2 = gHk2 in Eq. (23), which gives λ = k-1 = gH /f. The quantity, λ, which has unit of length, is called the (external) Rossby radius of deformation, which is of fundamental importance in the dynamics of rotating flows. 8 m s-2, H = 1 km and f = 10-4 s-1, so L ≈ 6300 km. It is evident that when waves are short compared with the Rossby radius, the pressure gradient or the gravity dominates the wave behavior, so the waves are non-dispersive, pure gravity, shallow water waves.