The interaction of an inhomogeneous vortex sheet with discrete vortices and flow

The dynamics of an inhomogeneous vortex sheet of finite length, interacting with point vortices and fluid flow in a two-dimensional ideal fluid, have been investigated theoretically. Exact solutions for the line density of the vortical sheet were obtained by transforming the general equations of motion into individual Cauchy-type integral equtions. On the basis of the obtained solutions, the uniform rotation of segments of the vortex sheet and point vortices in fluid flows of constant vorticity is described. It is shown that the integral equations may also be used to study the interaction of a frontal layer with discrete vortices in atmospheric frontogenesis models.