Nonlinear evolution of quasicircular flows (Q811234)

The authors study the two-dimensional ideal incompressible vortex flow model. A key role in this study is played by the method of ``slow'' variables known from radio physics, which is applied to the investigation of non-stationary solutions of the nonlinear system under consideration. Starting from an exact stationary solution, which describes purely rotational motion of the fluid, and, assuming this solution to be the ``generating'' solution, the authors extend it to the nonstationary and nonaxisymmetric case by using a small parameter that takes into accout the ``slowness'' of the variation of the functions with respect to the azimuthal angle and time. The investigation of the nonlinear transformation of a flow with initial stream-lines in the form of ellipses illustrates the capability of the proposed method.