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Center for Nonlinear Studies |
Recently, a generation of horizontal vortices by surface waves was observed experimentally. The story gained a lot attention, since the effect is impossible in the case of potential waves, the assumption commonly used in describing surface waves. In this talk we present a first-ever theory explaining the appearance of surface solenoidal currents. It turns out that the viscosity of a fluid plays a crucial role. It violates the potential flow assumption and determines the existence of non-zero vorticity, concentrated in a narrow viscous sublayer near the fluid surface and directed parallel to the surface. Then the nonlinear interaction of surface waves leads to the emergence of vorticity directed perpendicular to the surface: One can roughly say that the surface tilt produces a tilt of the vorticity in the viscous sublayer as well. Surprisingly, the expression for the velocity associated with the surface solenoidal currents is independent of viscosity, though it is produced by the viscous mechanism --- a novel example of the so-called ‘’viscous anomaly’’ in fluid mechanics. The theory was checked experimentally for the simplest case of two orthogonal plane waves. In particular, we showed that an amplitude of vertical vorticity is proportional to the squared surface tilt, the consequence of nonlinear origin of vorticity, and we was able to predict nontrivial spatial distribution of surface currents.
Host: Misha Chertkov