Volume 21: Pages 252-259, 2008
Wind wave frequencies decrease during growth and decay
Kern E. Kenyon 1
14632 North Lane, Del Mar, California 92014-4134
A physical model is applied to the initiation of surface gravity waves on a level air-sea interface by a steady wind that started up suddenly. The approach, believed to be new, is based on the two balance equations for linear and orbital angular momentum; the normal energy balance equation is not used. As a consequence the two governing equations in the two unknowns, amplitude and frequency, are first order, nonlinear, and coupled. An analytical solution to these equations has been found by separating out the time variable raised to a power, which turns out to be either an integer or a rational number. The amplitude is calculated to increase and the frequency to decrease simultaneously with increasing time, qualitatively consistent with fetch-limited waves. One characteristic of the wave solution, not shared by available growth theories, is that the average steepness of the wave surface stays fixed during growth. A quantitative comparison with observations of fetch-limited waves shows that the present theory predicts a faster amplitude growth rate than the measurements indicate but that the theoretical rate of frequency downshift is in better accord with the data. By a similar method applied to the frictional decay of gravity waves, it is found that both the predicted decrease in amplitude and decrease in frequency with increase in time agree with observations of waves that traveled halfway around the world.
Keywords: Surface Wave Growth, Surface Wave Decay, Frequency Downshifting
Received: September 9, 2007; Accepted: October 11, 2008; Published Online: February 6, 2009