DAMPING OF GRAVITY WAVES 

 BY SURFACE FILMS 



John W. Miles 



Institute of Geophysics and Planetary Physics 



University of California, San Diego 



La Jolla, California 



INTRODUCTION 



We consider the damping of gravity waves in the presence of surface con- 

 tamination. Our primary goal is an estimate of the effect of such contamination 

 on the generation of waves by wind on an unbounded surface; however, in order 

 to facilitate comparison with laboratory experiments, we consider waves in a 

 cylindrical basin, with an unbounded surface as a limiting case. We give rather 

 more detailed results for the surface-film damping coefficient than is warranted 

 by our present knowledge of the physical parameters, and in the final analysis 

 we consider only the limiting cases of an uncontaminated surface and an inex- 

 tensible film. We find that the minimum wind speed required to initiate waves 

 of significant magnitude on a contaminated surface may be roughly an order of 

 magnitude larger than for a clean surface. This conclusion is consistent with 

 the available observations. 



Let k and o- denote the wave number and angular frequency of an oscillation 

 determined on the hypothesis of an inviscid liquid, and let v be the kinematic 

 viscosity of the actual liquid. Then l k is an appropriate length scale for the 

 irrotational component of the velocity field, and 



§ = (2v/cr)l/2 _ (1) 



the thickness of the boundary layer on an oscillating flat plate, is an appropriate 

 length scale for the viscous component. We base our discussion on the hypo- 

 thesis that 



e := kS « 1, kh, (2) 



where h is the mean depth of the liquid. The dispersion relation between cr and 

 k then is 



0-2 = gk tank kh [1 + 0(e)] , (3) 



where g is the acceleration due to gravity. 



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