Nonlinear behaviour of interacting mid-latitude atmospheric vortices

Nonlinear behaviour of interacting large-scale atmospheric vortices is considered. These vortices are approximately fifteen kilometres high and can have diameters of hundreds if not thousands of kilometres, and so they can be thought of as large flat structures. The air is weakly compressible, and the fluid motion is subject to the Coriolis pseudo-force, due to the Earth being in a non-inertial rotating reference frame. The vortices studied are coupled binary systems. The high or low pressure in each vortex is modelled initially using an exponential function. A spectral method is presented, for obtaining accurate numerical solutions. Nonlinear results in the f-plane approximation are discussed at mid-latitudes. It is found that the vortices do or do not interact, depending on their initial radii and the location of their centres. A scaling law is found numerically for the ratio of these two quantities, which determines whether interaction does occur.