VII-th International Conference "SOLITONS, COLLAPSES AND TURBULENCE: Achievements, Developments and Perspectives" (SCT-14) in honor of Vladimir Zakharov's 75th birthday
August, 04-08, 2014
Chernogolovka, Russia

Formation of singularities at the interface of two fluids as a result of the Kelvin-Helmholtz instability
Date/Time: 14:40 05-Aug-2014
The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small interface angle approximation (gravity and capillary forces are neglected) admit exact solutions in the implicit form. The analysis of these solutions shows that, in the general case, weak root singularities are formed on the interface in a finite time for which the curvature becomes infinite, while the slope angles remain small. For Atwood numbers close to unity in absolute values, the surface curvature has a definite sign correlated with the boundary deformation directed towards the light fluid. For fluids with comparable densities, the curvature changes its sign in a singular point. In the particular case of fluids with equal densities, the obtained results are consistent with those obtained by Moore based on the Birkhoff-Rott equation analysis.

Zubarev Nikolay Mihailovich (Presenter)
(no additional information)

Kuznetsov Evgenii A.
(no additional information)

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