Evolution of gravity waves through resonant and nonresonant interactions in a dissipative atmosphere

Details Evolution of gravity waves through resonant and nonresonant interactions in a dissipative atmosphere Evolution of gravity waves through resonant and nonresonant interactions in a dissipative atmosphere

Feb 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jastp..59..305y&link_type=abstract

Journal of Atmospheric and Terrestrial Physics, v. 59, p. 305-317.

Physics

5

Scientific paper

We examine the evolution of three-gravity-wave interactions, with one initially much stronger than the other two, in a dissipative atmosphere. The characteristic time is used as an essential time scale for depicting the interactions. In the absence of viscosity, the solutions of the linearized interaction equations, viz., the parametric instability, give a good description for the evolution of secondary waves up to one-half of the characteristic time. Beyond this time, the linear solutions are invalid; the evolution must be obtained by solving the complete interaction equations. For given initial wave amplitudes, the characteristic time increases with the increasing wavelength of the primary wave; thus the criterion for the validity of resonant interaction approximation may be better satisfied. The viscous dissipation makes the characteristic time larger, and when severe enough a portion of the secondary waves, particularly at high wavenumbers, may fail to interact with the primary wave effectively. Additionally, the maxima of the energy densities for the secondary waves are smaller than those in the absence of viscosity. In the case of a significant frequency mismatch, only a fraction of the primary wave energy takes part in the interchange.

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