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Direct Numerical Simulation of Wave‐Mean Flow and Wave‐Wave Interactions: a Brief Perspective
Book chapter

Direct Numerical Simulation of Wave‐Mean Flow and Wave‐Wave Interactions: a Brief Perspective

C‐L Lin, J. R Koseff, J. H Ferziger and S. G Monismith
Physical Processes in Lakes and Oceans, pp.271-284
Coastal and Estuarine Studies, volume 54, American Geophysical Union
01/01/1998
DOI: 10.1029/CE054p0271

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Abstract

In this paper we examine the interaction of internal waves with the critical layer and the role of the parametric subharmonic instability (PSI) in the energy transfer process when multiple triad interactions are generated by one strong primary mode and background white noise or a Garrett‐Munk (GM79) model spectrum. We performed direct numerical simulations of the incompressible Navier‐Stokes equations with the Boussinesq approximation, using the pseudo‐spectral method (see Rogallo, 1981, Holt et al., 1992). For the critical layer a spanwise Rayleigh‐Taylor instability should be the most unstable mode if the Richardson number is less than zero locally. The mixing efficiency associated with this process still remains an open question. For the triad interactions the PSI energy transfer mechanism is feasible if local sum resonance is suppressed (i.e. under certain geometric constraints), but it is not clear if the mechanism is resonant. When examining triads with a background GM79 spectrum we found that even when the energy level of the spectrum was reduced by a factor of 100 the induced diffusion triads (non‐resonant) were the strongest, indicating the dominance of wave‐mean flow interactions. In this instance triads of the PSI type were still not found, suggesting that they may not be significant in the distribution of wave energy in the ocean.
 Wave‐mean flow interaction Parametric subharmonic instability (PSI) Direct numerical simulations (DNS) Pseudo‐spectral method Wave‐wave interactions

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