phase with the oscillations of the 20°, 17° and 15.5° isotherms located in 

 the main part of the thermocline . 



A systematic phase shift of the inertial wave with depth would not alter 

 the power spectra, nor cause the apparent frequency shift seen in Figure 7. 

 Further analysis of the series will be carried out in an attempt to deter- 

 mine if the apparent frequency shift is real or artifact. 



A power spectrum of the 20° isotherm was also computed for frequencies 

 between and 5 CPH without lopass filtering. The area under the curve, in 

 the low frequencies, .014 to .11 CPH (72 to 9-hr. periods) accounted for .65 

 of the total power. In the higher frequencies, between .11 and .4 CPH (9 to 

 2.5-hr. periods), there was .24 of the total power and between .4 and 5 CPH 

 (2.5 hr to 12 min . periods), .11. There were several small but statisti- 

 cally non-significant peaks in the high frequencies between .42 and .12 CPH 

 (2.4 and 8-hr. periods). 



If the assumption is made that the semi-diurnal period internal waves 

 revealed by the power spectra are progressive waves, a calculation based on 

 the observed density distribution and on Fjeldstad's (1933) theory of inter- 

 nal waves would give a wave velocity of 92 cm/sec., and a wave length of 

 22 nm. 



The auto-correlation functions for selected isotherms for lags between 

 6 minutes and 20 hours are shown in Figure 8. The three curves show sharp 

 drops to minimum correlations at 6 hours, then increase to peaks between 12 

 and 13 hours . The values of the auto-correlation function in this peak 

 range from 0.46 to 0.54. Not shown in the figure are the curves for the 17° 

 isotherm, which is very close to that of the 12.5° isotherm, and the curve 

 for the 15.5° isotherm which falls mid-way between the curves of the 12.5° 

 and 14° isotherms . The dominance of the semi-diurnal period at all depths 

 is clearly shown by these auto-correlation curves . It is also noteworthy 

 that within two hours the correlation has decreased to values near 0.5, or 

 approximately to those of the functions in the 12 to 13-hr. peak. 



The variability of the depth of the thermocline is further demonstrated 

 in Figure 9 by curves showing the percentage of occurrence of depth differ- 

 ences of the 20° isotherm computed for lags of 50 seconds to 1 hour. For a 

 50-second lag, ^0% of the time there was no change in depth between observa- 

 tions. For a lag of 1 hour, 5% of the time there was no change, and b% of 

 the time the difference was greater than 25 feet. 



From similar curves for the other selected isotherms, the percentages 

 of time that the depth changes exceeded 25 feet for lags of 1 hour were as 

 follows: 17°- 4f„; 15.5°-5'/„; 14.0°- 9f„; and 12.5°- 1%. Statistical sum- 

 maries of the lag differences for the selected isotherms are given in Tables 

 4, 5, 6, 7 and 8. Note that the standard deviations for lags of 1 hour are 

 approximately one-half as large as the standard deviations computed for the 

 entire series, listed in Table 2. 



419 



