Homogeneous intrusions in a rotating stratified fluid

A study is made of intrusions of fixed volumes of fluid of constant density into a uniformly stratified and uniformly rotating environment. In particular, the eventual steady-state configuration is sought for the ideal fluid case. Exact two-dimensional solutions can be found using a co-ordinate transformation which converts the equations satisfied outside the intrusion into the Cauchy-Riemann equations. The same technique does not, however, yield linear equations in the axisymmetric case. Effects of friction are also considered for cases where the quasi-geostrophic approximation can be made. Vertical advection by the viscosity-induced motion is shown to have the same effect on the temperature field as a greatly enhanced lateral diffusion, and therefore tends to spread the intrusion out laterally.