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Center for Nonlinear Studies |
I consider two different situations. First, formation of coherent vortices by an inverse cascade in 2d turbulence in a restricted vessel is analyzed. Second, we analyze production of vortices by waves excited on a fluid surface. An inverse turbulent cascade in a restricted two-dimensional periodic domain leads to the creation of condensate -- a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out detailed theoretical analysis based upon momentum and energy exchanges between the turbulence fluctuations and the mean coherent condensate (vortices). We show that the vortices have a universal internal structure. The theory predicts the vortex core profile and also the amplitude which perfectly agree with the numerical data. Phys. Rev. Lett. 113, 254593 (2014). At some conditions the non-linear interaction of the waves excited on a fluid surface leads to formation of vortices on the surface. The shape of the vortices is determined by the wave's shape and the depth of their penetration to the fluid is determined by the wavelength (in contrast to the well-known thin viscous layer of the waves).
Host: Michael Chertkov