TY - JOUR
T1 - Viscous effects on wave generation by strong winds
AU - Zeisel, A.
AU - Stiassnie, M.
AU - Agnon, Y.
N1 - Funding Information:
This research is part of an MSc thesis submitted by A. Z. to the Graduate School at the Technion – Israel Institute of Technology. The research was supported by The Israel Science Foundation (Grant 695/04) and by the Fund for Promotion of Research at the Technion.
PY - 2008/2/25
Y1 - 2008/2/25
N2 - This paper deals with the stability of water waves in a shear flow. Both temporal and spatial growth rates are derived. A carefully designed numerical solver enables us to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a friction-velocity of 1 m s−1). The main finding is the appearance of a second unstable mode which 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 18 cm 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.
AB - This paper deals with the stability of water waves in a shear flow. Both temporal and spatial growth rates are derived. A carefully designed numerical solver enables us to extend the range of previous calculations, and to obtain results for larger wavelengths (up to 20 cm) and stronger winds (up to a friction-velocity of 1 m s−1). The main finding is the appearance of a second unstable mode which 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 18 cm 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.
UR - http://www.scopus.com/inward/record.url?scp=39049111444&partnerID=8YFLogxK
U2 - 10.1017/S0022112007009858
DO - 10.1017/S0022112007009858
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SN - 0022-1120
VL - 597
SP - 343
EP - 369
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -