On three-dimensional internal gravity wave beams and induced large-scale mean flows

• Published in: Journal of fluid mechanics Vol. 769; pp. 621 - 634
• Main Authors: Kataoka, T., Akylas, T. R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.04.2015
• Subjects: Amplitude; Beams (radiation); Boussinesq approximation; Boussinesq equations; Computational fluid dynamics; Fluids; Gravitation; Gravitational waves; Gravity; Gravity waves; Interactions; Internal waves; Laboratories; Mathematical models; Mechanical engineering; Propagation; Three dimensional flow; Wave propagation; geophysical and geological flows; internal waves
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2015.143

The three-dimensional propagation of internal gravity wave beams in a uniformly stratified Boussinesq fluid is discussed, assuming that variations in the along-beam and transverse directions are of long length scale relative to the beam width. This situation applies, for instance, to the far-field behaviour of a wave beam generated by a horizontal line source with weak transverse dependence. In contrast to the two-dimensional case of purely along-beam variations, where nonlinear effects are minor even for beams of finite amplitude, three-dimensional nonlinear interactions trigger the transfer of energy to a circulating horizontal time-mean flow. This resonant beam–mean-flow coupling is analysed, and a system of two evolution equations is derived for the propagation of a small-amplitude beam along with the induced mean flow. This model explains the salient features of the experimental observations of Bordes et al. (Phys. Fluids, vol. 24, 2012, 086602).