Contour dynamics with non-uniform background vorticity

In this paper it is demonstrated how a contour dynamics method can be used to simulate the behaviour of vortices in the presence of non-uniform background vorticity in general, and on the gamma -plane in particular. For standard contour dynamics in case of zero, or uniform background vorticity, the initial continuous vorticity distributions of the vortices are replaced by appropriate piecewise-uniform distributions. Then, the evolution of the contours separating the several regions of uniform vorticity, are followed in time. In the case of non-uniform background vorticity, it is necessary to replace the sum of the (relative) vorticity of the vortices and the background vorticity by a piecewise-uniform distribution. This has several consequences for applying the method of contour dynamics, which are discussed in this paper. The resulting method is tested on some numerical examples. One of them is (qualitatively) compared with laboratory experiments carried out in a rotating tank.