The dynamics of a columnar vortex in an imposed strain

Exact solutions of the time-dependent Euler equations are presented which correspond to uniform columnar vortices with elliptical cross sections undergoing rotation and deformation in a uniform three-dimensional straining flow. In this work, the recent solutions of Kida [J. Phys. Soc. Jpn. 50, 3517 (1981)] are generalized to include the effect of a strain component along the axis of the vortex which results in its stretching. The time-dependent solutions should play a very useful role in modeling time-dependent vortex interactions in more complicated flows such as the mixing layer.