MODULATION OF WIND RIPPLES BY LONG SURFACE-WAVES VIA THE AIR-FLOW - AFEEDBACK MECHANISM

The evolution of a short-wave (SW) spectrum along a long wave (LW) is studied. The evolution of the SW spectrum variation is treated in the relaxation time approximation. The variation of the SW spectrum is cau sed by the LW orbital velocities and by the variation of the wind stre ss along the surface of a LW. The latter is due to the distortion of t he flow by a LW, and to the variation of the roughness induced by the modulated short waves. This introduces a feedback mechanism: more SWs give rise to a larger roughness, which by increasing the local stress stimulates the growth of more SWs. It is shown that this aerodynamic f eedback effect dominates the modulation of the SW spectrum for moderat e and strong winds. The feedback mechanism is most effective for SWs i n the gravity-capillary range, increasing its dominance with increasin g windspeed and decreasing frequency of a LW. The maximum of the SW am plitude modulation is situated at the crest of a LW. The results are i n agreement with laboratory and field measurements of the short-wave m odulation.