573 



5. SOME EXAMPLES OF OBSERVATIONS OF FINITE AMPLITUDE 

 WAVES ALONG A SLOPING BOUNDARY 



By processing satellite data on sea surface infrared 

 emission one can see moving patterns of sea surface 

 temperature in the Gulf of Mexico between the con- 

 tinental shelf edge and the coast. 



A sequence of processed satellite images taken 

 one hour apart is shown in Figure 2. Because the 

 mean current, U, at the time of observation is not 

 known, one cannot say whether these waves satisfy 

 the dispersion relations for the kind of edge waves 

 discussed here. All one can say at this point is 

 that it appears possible to satisfy the dispersion 

 relations given with wavelengths , bottom slopes , 

 and currents of reasonable orders of magnitude, but 

 one needs to refine the observations further before 

 one can reach any definite conclusions. 



6. CONCLUSIONS 



Nonlinear edge waves of finite amplitude can have 

 dispersion relations defined by a set of equations 

 relating particle oscillation frequency, encounter 

 frequency, wave number, and other parameters in a 

 way that can be solved systematically if one starts 

 by specifying a suitable wave variable, in the pres- 

 ent case, frequency. 



The observations which inspired the present anal- 

 ysis show Gerstner edge waves or possibly waves of 

 a different kind; one cannot tell with the evidence 

 now at hand . 



ACKNOWLEDGMENT 



The research reported here was supported by the 

 Office of Naval Research under Contract No. N00014- 

 76-C-0413. The observations cited were made with 

 support from the Office of Naval Research under 

 Contract No. N00014-75-C-0291. The satellite images 

 were processed using the facilities of Air Force 

 Geophysics Laboratory, Lincoln, Mass. 



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