Baroclinic Instability - Numerical

Baroclinic Inversion/ Instability — Numerical Experiments This is a two layer version of the doubly–periodic, quasigeostrophic code we used to study Rossby waves and vortices. It solves the equations � � ∂ ∂ ∂ + U1 + J(ψ1 , ·) q1 + [β + F1 (U1 − U2 )] ψ1 = f ilter ∂t ∂x ∂x � � ∂ ∂ ∂ ψ2 = f ilter + J(ψ2 , ·) q2 + [β + F2 (U2 − U1 )] + U2 ∂t ∂x ∂x with the inversion formulae q1 = (∇2 − F1 )ψ1 + F1 ψ2 q2 = (∇2 − F2 )ψ2 + F2 ψ1 The model runs with the appropriate link on the Linux machines. For the inversion, you specify the parameters U1 , U2 , F1 , F2 , and β. Given the fields for q1 and q2 as functions of x and y, the program will calculate ψ and contour both the PV anomalies qi and the full PV fields qi + [β + Fi (Ui − U3−i )]y. It will also show the streamfunction anomalies ψi and the full streamfunction ψi − Ui y. Once you have specified the PV and/or streamfunction fields, use QG model to see how the flow evolves. The parameters are similar to those in the BT vorticity equation solver. Experiments to consider · Explore the relationship between upper layer PV anomalies and the flows in both layers. · Explore the instability criterion. · Show that stable waves can still amplify, at least temporarily, if the initial phase relationships between upper and lower layers are correct. · Examine the interaction of two blobs of anomalous PV, one upper layer and one lower. Figure out the conditions under which they will reinforce each other. (Hint — remember that the primary effect of the PV anomalies in linear theory is to advect the background PV gradients.) What happens in the nonlinear regime? · A growing plane wave is an exact solution to the equations above. What happens when such a wave is perturbed? Compare unperturbed to perturbed solutions.