Gravity turbulence connected with interfaces

The spectral distributions of turbulence, as generated by the gravity waves on the interface between two fluids, are investigated. Both stable and unstable surfaces are considered. An unstable surface refers to the early development of turbulence from the Taylor instability. A stable surface may refer to the sea-surface. A repeated-cascade method is used to close the hierarchy of correlations at their fourth order, and to determine the eddy transport property through a memory chain of eddy relaxations. The production, inertia and dissipation subranges of spectral distributions on an unstable surface with friction are found to follow the laws k⁻², k⁻³, and k⁻³ for the kinetic energy, and k^−3.5, k⁻¹, and k⁻⁵ for the surface elevation. The inertia, eddy dissipation by gravity, and molecular dissipation subranges on a stable surface with friction are found to follow the law k⁻³ for the kinetic energy, and the laws k⁻¹, k⁻⁵ and k⁻⁵ for the surface elevation, respectively. The effects of surface tension are also investigated.