Stochastic Dynamics of a Vortex Loop. Large Scale Stirring Force

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Stochastic dynamics of a vortex filament obeying local induced approximation equation plus random agitation is investigated by analytical and numerical methods. The character of a stirring force is supposed to be a white noise with spatial correlator concentrated at large distances comparable with size of the loop. Dependence of the spectral function <sκαsκβ> of the vortex line on both the one-dimensional wave vector κ and intensity of the external force correlator <ζκαζκα> was studied. Here sκα is the Fourier transform of the line element position sα(ξ, t). It is shown that under the influence of an external random force a vortex ring becomes a small tangle whose mean size depends on external force intensity. The theoretical predictions and the numerical results are in reasonable agreement.