## Track Model

The circumpolar midlatitude region is modeled as a reentrant channel on a beta-plane between two rigid lateral boundaries (— y < x < y and — \ < V < y)- domain is 30,000km long and 8,000 km wide. A steady external forcing is introduced to support a reference flow, which has a zonally nonuniform velocity field (uref, wref) with corresponding stream function ^ref and vorticity Zref, viz.

J(^ref, Cref + f)+ aZref = Forcing, where a is a friction coefficient, f = fo + f3y and J (A, B) = Ax By — Ay Bx is the Jacobian. We particularly prescribe a reference flow with two localized jets, which plays the role of a proxy forcing.

A localized westerly jet has cyclonic vorticity in its northern flank and anticyclonic vorticity in its southern flank. We therefore introduce a reference flow that has the following idealized distribution of vorticity:

Cref = X) A(j)y exp(—y2)Fj (x), (1) j=i where x and y are nondimensional coordinates with Fj (x) = 1 in two sectors, xW < x < xE, and Fj (x) = 0 elsewhere. In the special case of Fj (x) = 1 for the whole domain, the reference flow would be a zonally uniform Gausian jet centered at y = 0, namely uref = B exp(—y2), with B being its strength. The relative strengths and geometrical characteristics of the winter mean Pacific and Atlantic jets at an upper tropos-pheric level are used as a guide for prescribing A(j), xE and x^1. These two jets are referred to by superscripts j = 1 and j = 2 respectively.

Hence, (1) is the vorticity field of two approximately zonally oriented Gaussian jets separated by a distance (xW — xE )• Furthermore, since the vorticity is only a function of the spatial derivatives of the velocity components, a reference flow would not be completely prescribed until a domain average zonal wind component, uoo, is also specified. Then the stream function field of the reference state would be ^ref = —uooy + V~2Cref, which can be readily determined by inversion subject to well-known boundary conditions. There are quite a few parameters that specify the relative strength, length, shape, orientation and locations of the two idealized localized jets. It would be sufficient to focus on one particular set of parameter values that supports a reference flow that has the primary features of the observed time mean flow in the upper troposphere.

Distance, velocity and time are measured in units of L = 106 m, U = 60 ms-1 and LU= 0.17 x 105 s respectively. Hence, the nondimensional domain is —15 < x < 15 and —4 < y < 4. To mimic the relative strengths and lengths of the Atlantic and Pacific jets, we use = 0.7 and xj[)~xJ) = 0.6. We specifi-

xw = 4.9 and xyE' = 8.5. The nondimensional value of the variation of the Coriolis parameter with latitude in the extratropics is ¡3 = 0.229. A value of uoo = 0.2 is used as a representative additional domain average zonal velocity component corresponding to 12 m/s.

The nonlinear evolution of the flow in this model is governed by

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