1 / 8

CDV derivation

CDV derivation. The CDV model comprises a Rossby wave mode and uniform zonal flow over a mountain in a plane channel. The coriolis parameter f is approximated by f = f + y The flow is resticted by lateral walls with width 0< y<Lx and length 0<x<Lx.

odessa
Download Presentation

CDV derivation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. CDV derivation • The CDV model comprises a Rossby wave mode and uniform zonal flow over a mountain in a plane channel. • The coriolis parameter f is approximated by f = f + y • The flow is resticted by lateral walls with width 0< y<Lx and length 0<x<Lx. • The flow is also periodic in longitude so (x,y,t)= (x+Lx,y,t) Boundary conditions • No normal transport at the boundaries requires PHI to be constant at y= 0,Ly

  2. CDV Derivation • The equation used in the model is the QGPV equation • To derive the low order spectral model you must expand , , and h(x,y) into orthonormal eigenfunctions of the Leplace operator. • This derivation is very complex. I will show a more general representation by solving Leplace’s equation on a rectangle and introducing the concept of orthogonality.

  3. CDV Derivation • Laplace equation • Break the problem into four problems with each having one homogeneous condition • Separate the variables • Solve x dependent equation and y dependent equation. • Use boundary conditions and orthogonality to find coefficients

  4. CDV derivation • Orthogonality • Whenever it is said that functions are orthogonal over the interval 0<x<L. The term is borrowed from perpendicular vectors because the integral is analogous to a zero dot product

  5. CDV Derivation • The process is similar in the derivation of the CDV model • First you have to non-dimensionalize the QGPV equation.(A1,A2) • Represent h(x,y) and PHI* in terms of sines and cosines(A3), and expand PHI into three orthonormal modes(A4).

  6. CDV derivation • Insert A3 and A4 back into the A1. • This leads to the following equations known as the CDV equations. • The CDV equations are solved to find the equilibrium points

  7. CDV model • As we found from holton, the system has three equilibria point. One unstable and two stable(Show graphic again?) • For arbitrary initial conditions the phase space trajectories always tend to one of the two stable equilibria • This is a drawback of the CDV model because there is no way to transition between the two stable equilibra points.

  8. CDV model

More Related