TaylorGörtler vortices expected in the air flow on sea surface waves—II
 Masayuki Tokuda
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The instability of TaylorGörtler vortices which are expected in the air flow on water waves was studied in part I, under the assumption that the curvature around the crest or the trough of water waves, where the instability was expected to take place first, was constant, namely that the characteristics of the vortices were affected little by the local change of the curvature along the direction of the progress of water waves (the direction ofxaxis) However, the curvature actually varies from positive to negative, or vice versa. In order to study this effect, the instability of TaylorGörtler vortices is examined with respect to the range of the part of a constant curvature, in the model in which the curvature is positive constant near the trough and negative constant near the crest, and zero in the intermediate regions, respectively. It is shown that as the region of the constant curvature becomes narrower, the instability tends to weaken. For the same example with part I, namely, when the wind of 12.2 m s^{−1} is blowing over swells of 15 m in wavelength, if the range of constant curvature near the trough is taken as a quarter of one wave length, the critical wave height becomes 0.96 m instead of 0.50 m, and conversely, the wave length and the height of center of the vortex become 11.9 m and 2.1 m instead of 24 m and 3.7 m, respectively.
Further, using the energy equations, quantitative estimates are performed of the intensity of the vortices which develop when the wave height of the swell is 1.05 m in the above described example, and also of the influence of the vortices upon the wind profile when the equilibrium state is reached. When the vortices are generated and grow to attain to an equilibrium state interacting with the mean flow, the maximumxcomponent of velocity in the vortices is about 1.04 m s^{−1}. Consequently, the wind profile undergoes a considerable distortion from the logarithmic one near the level of 2 m height. This distorted wind profile has a form similar to those sometimes observed above the sea surface.
 Monin, A. S. andA. M. Yaglom (1971): Statistical Fluid Mechanics, Vol. 1, The MIT Press, Boston, pp. 160–203.
 Stuart, S. T. (1958): On the nonlinear mechanics of hydrodynamics stability. J. Fluid Mech.,4, 1–21.
 Tobak, M. (1971): On local Görtler instability. Z. Angew. Math. Phys.22, 130–143.
 Tokuda, M. (1972): TaylerGörtler vortices expected in the air flow on sea surface wavesI. J. Oceanogr. Soc. Japan,28, 242–253.
 Title
 TaylorGörtler vortices expected in the air flow on sea surface waves—II
 Journal

Journal of the Oceanographical Society of Japan
Volume 32, Issue 3 , pp 128138
 Cover Date
 19760501
 DOI
 10.1007/BF02107041
 Print ISSN
 00298131
 Online ISSN
 1573868X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Authors

 Masayuki Tokuda ^{(1)}
 Author Affiliations

 1. Geophysical Institute, Faculty of Science, Tohoku University, Aoba, Aramaki, 980, Sendai, Japan