Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous Fluid

Details Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous Fluid Exactly Integrable Dynamics of Interface between Ideal Fluid and Light Viscous Fluid

2004-07-09

arxiv.org/abs/physics/0407041v1

Physics Letters A, v.329, pp.49-54 (2004).

Physics

Fluid Dynamics

5 pages, 2 figures; submitted to Physics Letters

Scientific paper

10.1016/j.physleta.2004.06.073

It is shown that dynamics of the interface between ideal fluid and light viscous fluid is exactly integrable in the approximation of small surface slopes for two-dimensional flow. Stokes flow of viscous fluid provides a relation between normal velocity and pressure at interface. Surface elevation and velocity potential of ideal fluid are determined from two complex Burgers equations corresponding to analytical continuation of velocity potential at the interface into upper and lower complex half planes, respectively. The interface loses its smoothness if complex singularities (poles) reach the interface.

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