Nonlinear Dynamics of Curved Vortical Structures

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Vortices are important and fundamental structures in fluid dynamics. We clarify the effects of curvature on the behavior of vortices. The instability and nonlinear dynamics of a fat vortex ring, a helical vortex tube etc. are investigated theoretically ; the results are generalized to a general class of vortices which are curved. The effects of the axial flow, which exists in most of vortices, on the stability and nonlinear dynamics are also clarified by theoretical and numerical analysis. The obtained results are used to improve the statistical theory of turbulence.