Michael Stiassnie: Viscous Effects on Wave-Generation by Strong Winds

The talk deals with the stability of water waves in a shear flow. A carefully designed numerical solver enables to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a shear-velocity of 1 m/s). The main finding is the appearance of a second unstable mode which quite often turns out to be the dominant one. A comparison between results from the viscous model (Orr-Sommerfeld equations), and those of the inviscid model (Rayleigh equations), for 18cm long waves, reveals some similarity in the structure of the eigenfunctions, but a significant difference in the imaginary part of the eigenvalues (i.e. the growth-rate). It is found that the growth-rate for the viscous model is 10 fold larger than that of the inviscid one.

Michael Stiassnie er professor ved Technion, Israel