Munk 



hour and cycles per kilometer, respectively. It turns out that nearly all the en- 

 ergy is concentrated along two or three narrow bands, thus defining empirically 

 the corresponding Gij(k) relations. We have computed the corresponding rela- 

 tions for trapped edge waves, using the observed off-shore topography, and these 

 agree very satisfactorily with the empirical relations. There can be no doubt 

 that most of the energy is in the form of low-order trapped edge waves. Ap- 

 proximately equal energy travels up and down the coast. At the frequency under 

 consideration (cycles per hour), the effect of the Coriolis force leads to a slight 

 splitting of the co(k) curves. As one approaches daily frequencies, the situation 

 changes radically, and present remarks are not applicable. 



Finally, I wish to comment on an unexplained observation in the analysis of 

 tide records (Munk and Cartwright, 1966): the continuum spectrum peaks 

 sharply in the vicinity of the strong tidal lines. The explanation is not yet 

 known, but it appears that there are a number of processes that could be re- 

 sponsible for this peaking, and each of these might be important under some 

 circumstances. One is the nonlinear interaction of the low-frequency sea-level 

 oscillation with the tidal "carrier" frequencies, giving rise to modulated side 

 bands. Another is the relatively small surface effects associated with internal 

 tides, these being demonstrably incoherent with tide producing forces. And 

 finally, there is the effect of multiple line interaction under highly nonlinear 

 circumstances, such as a near bore situation. For this latter case, the peaked 

 spectrum is discrete, not continuous. 



This is an outline of an interesting set of problems. As the central frequen- 

 cies of the ocean wave spectrum have become populated, I find myself moving 

 monotonically towards lower frequencies. 



REFERENCES 



1. Snodgrass, F.E., Groves, G.W., Hasselmann, K.F., Miller, G.R., Munk, 

 W.H., and Powers, W.H., "Propagation of Ocean Swell Across the Pacific," 

 Philosophical Trans. Royal Soc. London A2 59:43 1-497 (1966) 



2. Barber, B.F., and Ursell, F., Philosophical Trans. Royal Soc. London A240: 

 527-560 (1948) 



3. Hasselmann, K., Munk, W., and MacDonald, G., "Bispectra of Ocean Waves," 

 in "Time Series Analysis," pp. 125-139, New York:Wiley, 1963 



4. Munk, W., Snodgrass, F., and Gilbert, F., "Long Waves on the Continental 

 Shelf," J. Fluid Mech. 20(Part 4):529-554 (1964) 



476 



