SECT. 5] INTERNAL WAVES 749 



from auto -correlation studies of the same' data, a tidal relation was definitely 

 disclosed. It was found that a significant correlation of wave depth occurred at 

 6.4 and 12.8 h, which were the exact lengths of semi diurnal tidal periods 

 (Fig. 20). This implies that the spectrum of Mave depth is sharply peaked at 

 the lunar semi-diurnal frequency. The fact that the phase changes then may 

 indicate that the waves are generated at a distance from the observing station 

 and suffer various phase lags in traveling from generator to receiver. 



j. Relation to basins and lakes 



It is likely that standing internal waves are present in bays, basins, and even 

 in lakes. Such waves are frequently related to the size and character of the lake. 

 In a two-layer rectangular bay of constant depth, the period of oscillation of a 

 free standing internal wave is (Wedderburn, 1909; Sverdrup, Johnson and 

 Fleming, 1942) 



uip-p') 



n 



_{pih)+{p'ihr 



where n is the number of standing wave nodes. 



An investigation conducted in the Gulf of California (February and March, 

 1939) indicated that the wavy character of the isobaric surfaces might be due 

 to the presence of a standing internal wave with a period between 6.3 and 7.65 

 days and probably closer to the former value (Sverdrup, 1940). The wave would 

 be of the first order with reference to the vertical axis (the vertical displace- 

 ment vanishing at the surface and bottom only) and with three nodes inside 

 the Gulf would be of the fourth order with reference to the horizontal axis. 



Within a standing internal wave, the horizontal velocity component reaches 

 a maximum near the nodes, so that only large-sized particles in the water 

 would settle in their vicinity. On the other hand, anti-nodes are characterized 

 by small horizontal currents, which would permit small particles to deposit on 

 the bottom. From the deposits in the Gulf of California, Revelle (1939) found 

 that the sediment varied in a regular manner along a north-south direction, 

 corresponding to an internal standing wave with three nodes. From the de- 

 posits, Revelle concluded that a standing internal wave of the fourth order was 

 not an isolated phenomenon but appeared to be of common occurrence in the 

 Gulf of California. 



Munk (1941) theoretically examined the Gulf of California to determine 

 whether any of the free internal-wave periods corresponded to the observed 

 internal-wave period. In this analysis the equation {loc. cit. p. 41) was extended 

 to take into account the geometric shape of the Gulf and the variation of 

 density. It was found that there were two periods, one of 7 days and the other 

 of 14.8 days. The observed distribution of density indicated that the first-order 

 wave (7 -day period) was dominant, but that the presence of the second-order 

 wave (14.8-day period) was not excluded. Munk's theoretical examination 

 fully confirmed Sverdrup's interpretation of observations in the Gulf of 

 California. 



