The motion of a 2-D vortex sheet in a background shear flow.

Abstract:

The planar vortex sheet in an uniform shear flow are considered. We use the same method as Krasny did in the study of vortex sheets, namely, Chorin's vortex blob method. A linear analysis shows that the background shear influences the motion of the vortex sheet in such a way that its stability characteristic with respect to low frequency modes are stabilized in some case. We examine this phenomena not only by the linear analysis but also by a numerical simulation of the nonlinear integral equation. In particular, we see carefully how the number and the location of the roll-ups of a vortex sheet change as the strength of shear does.

Conclusion:

The dynamics of vortex sheets in a shear flow is numerically simulated by the vortex method. The structure of singularities is qualitatively the same as that in the case of zero shear, when the shear works in the direction which strengthens the instability of the flat sheet. It is, however, quite different, when the shear works in the stable direction. Our computation seems to indicate that the number of singularities increases in time.

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Reference:

T. Sakajo and H. Okamoto, Numerical computation of vortex sheet roll-up in the back ground shear flow , Fluid Dynamics Research vol.17 (1996) p.195
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