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Homework Help: 3d rossby wave frequency dispersion relation

  1. Nov 22, 2008 #1
    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)=(nabla2 ψ+(f02/N2)*(d2 ψ/dz2)+bv

    where ψ is the horizontal streamfunction, f0 is the Coriolis parameter at the reference latitude, N2 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:

    2. Relevant equations

    3. The attempt at a solution
    tried many times but i actualy have no true direction

    thanks for any help
  2. jcsd
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