Repeated Cascade Theory of Gravity Turbulence with an Interface
Semi-annual technical rept. Jun-Dec 1971
CITY COLL RESEARCH FOUNDATION NEW YORK
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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 describe the eddy transport property as 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 for the kinetic energy and surface elevation. The inertia, eddy dissipation by gravity, and molecular dissipation subranges on a stable surface with friction are found to follow the law for the kinetic energy, and the laws for the surface elevation. The spectra with surface tension are also investigated. The physical parameters and the numerical coefficients are determined analytically.
- Fluid Mechanics