1971
DOI: 10.1017/s0022112071002635
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Non-linear resonant instability in boundary layers

Abstract: An investigation is made of resonant triads of Tollmien-Schlichting waves in an unstable boundary layer. The triads considered are those comprising a two-dimensional wave and two oblique waves propagating at equal and opposite angles to the flow direction and such that all three waves have the same phase velocity in the downstream direction. For such a resonant triad remarkably powerful wave interations take place, which may cause a continuous and rapid transfer of energy from the primary shear flow to the dis… Show more

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Cited by 432 publications
(175 citation statements)
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“…Based, in part, on pioneering attempts at nonlinear theories e.g., Benney and Lin, 1960;Craik, 1971, Orszag and Patera 1980, 1983 by n umerical experiments and Herbert 1984 by theory discovered a secondary instability mechanism. Herbert's 1984 theory is based on Floquet theory and accounts for an experimentally observed three-dimensional 3-D instability.…”
Section: Introductionmentioning
confidence: 99%
“…Based, in part, on pioneering attempts at nonlinear theories e.g., Benney and Lin, 1960;Craik, 1971, Orszag and Patera 1980, 1983 by n umerical experiments and Herbert 1984 by theory discovered a secondary instability mechanism. Herbert's 1984 theory is based on Floquet theory and accounts for an experimentally observed three-dimensional 3-D instability.…”
Section: Introductionmentioning
confidence: 99%
“…behavior with large growth rates that occur in both the fundamental and subharmonic types of breakdown, while Craik's resonant triad model [21] predicts an instability of the subharmonic type. Craik's mechanism (referred to as C-type) is thought to dominate at low amplitude of the TS wave, while Herbert's subharmonic mechanism (referred to as H-type) reflects the situation at moderate amplitudes of the TS wave.…”
mentioning
confidence: 99%
“…The most probable explanation of the found law in spectra of Fourier amplitudes of stationary streamwise vortices should be counted three-wave resonant interaction. Analog phenomena was investigated by Craik [5] for disturbances in boundary layer.…”
Section: Figmentioning
confidence: 99%