SECT. 5] LONG OCEAN WAVES 657 



277/n, from the outer edge of the continental slope. The jth harmonic is charac- 

 terized by J nodal lines, that isji values of .r in the interval x^O to x = A + B for 

 which the wave amplitude vanishes. The first theoretical discussion of edge 

 waves is due to Stokes (Lamb, 1932, p. 446) who derived the solution for the 

 fundamental mode. Ursell (1952) extended the solution to harmonics and 

 demonstrated their existence in the laboratory. For periods approaching 12 

 pendulum hours the effect of the Coriolis force is important (Reid, 1958; 

 Kajiura, 1958), and the solution merges with that of a Kelvin edge wave which 

 depends essentially on the earth's rotation (Crease, 1955). 



From an inspection of the power spectrum alone it is impossible to decide to 

 what extent the spectral density is associated with the continuous or discrete 

 part of the spectrum. Cross-spectra between records at variable long-shore 

 separation could resolve the problem in principle. Recordings at La Jolla and 

 Oceanside, 38 km apart along the coast of southern California, are in phase and 

 coherent for frequencies belpw 1 c/ks (Munk, Snodgrass and Tucker, 1959, 

 chart 10.2), whereas for the case of edge waves some measurable phase dif- 

 ferences are to be expected. This favors shelf waves. On the other hand there 

 have been isolated instances resembling edge-wave activity. Resurgences 

 following hurricanes traveling northward along the American east coast 

 (Redfield and Miller, 1957) give the appearance of an "edge-wave wake" 

 (Munk, Snodgrass and Carrier, 1956; Greenspan, 1956) but this interpretation 

 has not been universally accepted. Edge waves along the Great Lakes have 

 been described by Ewing, Press and Donn (1954), Donn and Ewing (1956) and 

 Donn (1959). Cross-spectra between a coastal station and an island station 

 100 km offshore indicate comparable energies in the continuous and discrete 

 parts of the spectrum (Snodgrass et al., 1961). 



Fig. 7 is, of course, highly schematic, but it serves to illustrate what we 

 believe to be the principal classification of the subject of long waves, namely the 

 separation into trapped and leaky modes. The chief weakness of the presentation 

 lies in the assumption of straight parallel contours, i.e. h = h{x) extending to 

 infinity along the ?/-axis. If the shelf were bounded by protruding headlands at 

 y— —\D and y— -\-\D, then only discrete values of n are permissible, namely 

 n = (2Z))-i, 2(2i))-i, 3(2i))-i, . . . The trapped modes now consist of a series 

 of points. For the actual continental shelf, the roughness of the coastline 

 must be associated with scattering of trapped energy into the leaky modes, and 

 vice versa, and the distinction loses sharpness. We concluded that the relative 

 contribution of the discrete and continuous parts of the spectrum to the 

 observed long-period activity is in doubt ; the existence of sharp spectral peaks 

 probably favors the continuum to be the predominant contributor. 



E. Discussion 



Some remarks concerning the causes of the shelf waves need to be made. 

 The spectrum ashore may be radically shaped by the shelf resonances. Still, 

 that does not explain what caused the oscillations in the first place. 

 22— s. I. 



