Abstract
A Hamiltonian version has been formulated for the model of a potential jet stream of a homogeneous incompressible fluid with a free boundary. In the framework of this model, instability regimes have been analyzed. It has been shown that self-similar solutions with a compact support can be dominant structures. Analysis of the instability mechanism shows that two collapse scenarios are possible. The first scenario occurs without the deformation of the shape and leads to an intensification of the vortex sheet according to the law (t 0 − t)−1, where t 0 is the collapse time. The second scenario leads to the formation of a singularity for the surface shape and to a decrease in the intensity of the vortex sheet according to the laws (t 0 − t)−1/5 and (t 0 − t)1/5, respectively. The integral collapse criterion has been found.
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Original Russian Text © V.P. Goncharov, 2009, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 89, No. 8, pp. 457–462.