The Response of Hill's Vortex to a Small Three Dimensional Disturbance

The response of Hill's vortex to a small three dimensional disturbance is examined. The perturbed field is expanded by the spherical solid harmonics Y(nm) and a system of equations for the evolution of the expansion coefficients is obtained. It is shown that these equations are closed for each azimuthal number m. In a case of axisymmetric distortion, Moffatt and Moore (1978) showed that if the initial disturbance is such as to make the vortex prolate spheroidal, rotational fluid is detrained, forming a thin spike at the rear stagnation point, and if the vortex is initially oblate, irrotaional fluid is entrained there. When the initial distortion is not axisymmetric, numerical results for m - 2 show that a peak of initial surface elevation moves downstream toward the rear stagnation point forming a spike-like structure.