An Analysis of Turbulent Motions In and Around a Differentially Forced Density Interface |
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Authors: | PC Wu HJS Fernando |
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Institution: | (1) Environmental Fluid Dynamics Program, Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, U.S.A., US |
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Abstract: | The Rapid-Distortion-Theory-based analysis proposed by Fernando and Hunt 1] is extended to study the nature of turbulence
in and around a density interface sandwiched between turbulent layers with dissimilar properties. It is shown that interfacial
motions consist of low-frequency, resonantly excited, nonlinear internal waves and high-frequency, linear internal waves driven
by background turbulence. Based on the assumptions that (i) all resonant waves and some nonresonant waves having frequencies
close to the resonant frequencies grow rapidly, break, and cause interfacial mixing, (ii) the spectral amplitude of the vertical
velocity in the wave-breaking regime is constant, and (iii) kinetic energy is equipartitioned between linear and nonlinear
breaking wave regimes, the r.m.s. vertical velocity at the interface and the turbulent kinetic energy flux into the interface
are calculated. The migration velocity of the interface is calculated using the additional assumption that the buoyancy flux
into a given turbulent layer is a fixed fraction of the turbulent kinetic energy flux supplied to the interface by the same
layer. The calculations are found to be in good agreement with the entrainment data obtained in previous laboratory experiments
in the parameter regime where the interface is dominated by internal wave dynamics.
Received 23 July 1997 and accepted 8 January 1999 |
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