Modeling of barotropic fluid dynamics on the sphere based on the contour dynamics (Q2760705)

To study numerically the barotropic fluid motion on a sphere, the author uses the method of contour dynamics which was introduced as a technique for solving nonlinear two-dimensional Euler equations. The main advantage of this method is that it is possible to reduce the dimensions of the problem under consideration and, in addition, to solve problems with non-smooth initial data. In the article under review, it is shown how this concept may be applied to study the motion and interaction of some vortex structures on a sphere. With the help of the so-called contour surgery suggested by \textit{D.~Dritschel} in [J. Comput. Phys. 77, No. 1, 240--266 (1988; Zbl 0642.76025)], the author constructs a numerical algorithm for solving the problem, and the rest of the article is devoted to numerical experiments.