LOW-FREQUENCY TAIL OF THE 

 OCEAN WAVE SPECTRUM 



Walter H. Munk 



Institute of Geophysics and Planetary Physics, La Jolla Laboratories 



University of California, San Diego 



La Jolla, California 



I will review briefly four relatively new observations concerning ocean 

 waves whose frequency is below that of ordinary wind waves. The topics are 

 vaguely related and they emphasize the importance of nonlinear processes. 



At 2 to 3 cycles per minute one occasionally finds well-developed spectral 

 peaks associated with swell from distant storms. These peaks shift from day to 

 day toward higher frequency, and the rate of shift gives information concerning 

 source time and distance. 



One new development concerns an attempt by Snodgrass et al. (1) to meas- 

 ure waves simultaneously at widely separated points. These measurements 

 confirm nicely what had already been fairly clear since the days of Barber and 

 Ursell (2): each wave component moves at a group velocity appropriate to its 

 frequency. The purpose of the experiment was to measure the attenuation of the 

 ocean waves. They diminish rapidly in the near zone (within one storm diame- 

 ter) and very slowly thereafter. The behavior can be accounted for in terms of 

 "Stokes scattering": interacting wave groups from the storm area scatter en- 

 ergy into high frequencies, where they are ultimately removed by white capping. 

 From what we know of scattering cross sections, there is no insuperable quan- 

 titative discrepancy. The super -exponent behavior follows from the fact that 

 the interaction depends on the products of the interacting amplitudes, on the 

 beamwidth, and on the bandwidth in the frequency domain; all these quantities 

 diminish with distance from the storm area. 



So far we have been concerned with nonlinear interactions leading to higher 

 (sum) frequencies. Insofar as these interactions lead to difference frequencies, 

 one can explain to some extent oscillations at around 1 cycle per minute, which 

 have been observed with appropriate instrumentation (3). 



Further down the frequency scale I would like to refer to one of the few 

 clear-cut results in some long-time efforts to make sense of the low-frequency 

 oscillations (4). We used an array of instruments separated by various dis- 

 tances along shore, ranging from 1/2 mile to 20 miles. By a suitable analysis 

 one can find the description of wave energy in o), k-space, where a; is the tem- 

 poral frequency and k is the spacial frequency. Suitable units are cycles per 



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