Abstract
The evolution of a short-wave (SW) spectrum along a long wave (LW) isstudied. The evolution of the SW spectrum variation is treated in therelaxation time approximation. The variation of the SW spectrum is caused bythe LW orbital velocities and by the variation of the wind stress along thesurface of a LW. The latter is due to the distortion of the flow by a LW, andto the variation of the roughness induced by the modulated short waves. Thisintroduces a feedback mechanism: more SWs give rise to a larger roughness,which by increasing the local stress stimulates the growth of more SWs. It isshown that this aerodynamic feedback effect dominates the modulation of theSW spectrum for moderate and strong winds. The feedback mechanism is mosteffective for SWs in the gravity-capillary range, increasing its dominancewith increasing windspeed and decreasing frequency of a LW. The maximum ofthe SW amplitude modulation is situated at the crest of a LW. The results arein agreement with laboratory and field measurements of the short-wavemodulation.
Published Version
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