REMARKS ON THE OCEAN WAVE SPECTRUM * 



W. H. Munk 

 Institute of Geophysics and Scripps Institution of Oceanography, University of 



California 



M. J. Tucker 

 National Institute of Oceanography, Surrey, England 



F. E. Snodgrass 

 Scripps Institution of Oceanography, University of California 



ABSTRACT 



A record of water level against time at a fixed point off La Jolla can be in- 

 terpreted as the result of superposition from waves of all possible frequencies. A typical 

 analysis into component frequencies shows five distinct bands of activity with frequen- 

 cies higher than those of the tides: ripples around 20 c/s, ordinary gravity waves 

 around 0.1 c/s, a narrow band of swell at 0.065 c/s, "surf beat" around 0.015 c/s (due 

 to non-linear transformation of ordinary waves in shallow water), and surges with 

 frequencies around 0.001 c/s. Quantitative estimates of energy density are given. The 

 measurement of the directional properties of waves is discussed in some detail. 



INTRODUCTION 



"Remarkable progress would be attained if only naval architects and ocean- 

 ographers would get together and study ship motion at sea." You may have come across 

 statements like this; they frequently appear in the literature of the last hundred years. 

 Offhand this sounds quite reasonable. But we doubt whether the proposed marriage 

 of the two professions would have resulted in a healthy offspring if it had taken place 

 prior to the last decade. The oceanographer simply could not offer an adequate de- 

 scription of the sea surface. 



The latest and most successful of matchmakers is J. King Couper of the Bureau 

 of Ships. We think his success is due, at least in part, to the circumstance that we are 

 now more than halfway towards an adequate description of the surface in terms of 

 the energy spectrum. The first step was to resolve the sea surface at a point in terms 

 of elementary wave trains of various frequencies, but regardless of wave direction. This 

 has been done. The next step is to obtain the directional pattern as well. Work on 

 this problem is underway. When it has succeeded, an important goal will have been 

 attained: the two-dimensional spectrum of the sea surface. 



Two reviews have recently been published: Pierson (1955) emphasizes how 

 much is known about what waves are like; and Ursell (1956) insists that nothing is 

 known about how they are generated. Our remarks will be confined to a few selected 

 topics: first a few basic (and well known) features of ocean wave spectra; then low 

 frequency waves, because we find them interesting; and finally, the directional spectrum, 

 because it is an urgent topic. 



* Contributions from the Scripps Institution of Oceanography, New Series, No. 950. 



45 



