William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
The temporal evolution of a resonant triad of wave components in a parallel shear flow has been investigated at second order in the wave amplitudes by Craik (1971) and Usher & Craik (1974). The present work extends these analyses to include terms of third order and thereby develops the resonance theory to the same order of approximation as the non-resonant third-order theory of Stuart (1960, 1962). Asymptotic analysis for large Reynolds numbers reveals that the magnitudes of the third-order interaction coefficients, like certain of those at second order, are remarkably large. The implications of this are discussed with particular reference to the roles of resonance and of three-dimensionality in nonlinear instability and to the range of validity of the perturbation analysis. © 1975, Cambridge University Press. All rights reserved.
William Hinsberg, Joy Cheng, et al.
SPIE Advanced Lithography 2010
Shiyi Chen, Daniel Martínez, et al.
Physics of Fluids
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
Michiel Sprik
Journal of Physics Condensed Matter