(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the linearized, quasi-geostrophic vorticity equation on the beta-plane,

with a mean background flow umean , which allows for vertical structure and propagation of Rossby waves:

(d/dt+umean*d/dx)=(nabla^{2}ψ+(f_{0}^{2}/N2)*(d^{2}ψ/dz^{2})+bv

where ψ is the horizontal streamfunction, f_{0}is the Coriolis parameter at the reference latitude, N^{2}the Brunt-Vaisala frequency, b is the beta parameter, and v is the meridional velocity component given by v =dψ/dx.

Assume a solution of the form ψ(x,y,z,t) = ψ_{0}e^{i(kx+my+nz-_t)}where k, m, n are the wavenumbers in the x, y, z directions, respectively.

Show that the frequency dispersion relation is given by:

ω=umean-b/(k^{2}+m^{2}+n^{2}(f_{0}^{2}/N^{2}))

2. Relevant equations

3. The attempt at a solution

tried many times but i actualy have no true direction

thanks for any help

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# Homework Help: 3d rossby wave frequency dispersion relation

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