6C/C = 0.7xlO'' 



for ;/ = 1 cm/sec, at all depths 



FIG. 10. Profiles of vertical displacement ? (left) and hori- 

 zontal velocity u (right) for surface (mode 0) and internal 

 (1,2) tides. Scale is arbitrary. 



pilations ). For the internal continuum estimates are 

 based on a recent version of the GM75 model. * All 

 phases are considered random, and so the totals are 

 summations in squared amplitudes. Actual values de- 

 pend on the local temperature and salinity prjjfiles, and 

 vary considerably from place to place. Mode numbers 

 refer to the number of zero crossings of the horizontal 

 current jt(z){Tig. 10). Here we distinguish between sur- 

 face tides (mode 0) with a uniform current from top to 

 bottom, and internal waves and tides (modes 1, 2, . . . ). 

 Surface tides have wave lengths of 3000 km, internal 

 tides 100, 60 km for modes 1, 2. Surface tides are 

 known to be sharply peaked at A/j frequency; internal 

 tides are intermittent and broadened. 



The sound velocity is perturbed by both vertical dis- 

 placement and horizontal currents: 



6C/C=(10, 1, 0.01)xlO-= 



for J = l m, at depths of 0.1, 1, 4 km , 



For surface tides it would appear that for a typical ray 

 path the u effect dominates, but for internal waves and 

 tides the J effect clearly dominates except at abyssal 

 depths. Further, most of the u energy (but only a frac- 

 tion of the J -energy) is at inertial frequencies, yet we 

 will show that there is no discernible inertial peak in 

 the acoustical spectra. 



To study tidal and inertial effects we need to analyze 

 the acoustic records at high resolution. Accordingly 

 the records were divided into the initial and final one- 

 half months (somewhat overlapping for Bermuda), and 

 the spectra computed for each harmonic. In this way 

 the spectra are computed at precisely the frequencies 

 of major tidal constituents. The two spectra are com- 

 bined for obtaining the average power in each band. 

 The statistical reliability is manifestly poor; there are 

 only two degrees of freedom in the fortnightly analysis, 

 and somewhat less than four degrees in the combined 

 analysis. Phase spectra (Table V) show a significant 

 semidiurnal tidal peak, Cartesian spectra (Table Vn) 

 do not. (' spectra likewise have no tidal peak.) We 

 estimate 2.5 square cycles (subtracting background) in 

 the semidiurnal <1> peak at Bermuda, as compared to a 

 total variance of 35 square cycles (excluding subinertial 

 drift). For the important 6$ spectrum, tides account 

 for 4x10'^ square cycles out of a total of 60x10'^ 

 square cycles. 



The simplest interpretation is that the current asso- 

 ciated with surface tides [wavelength 3000 k>}i) co- 

 herently modulates phase along all paths. The travel 

 time R/ C is modified by a fraction u/ C, and 



A* = 2t!(jWc) (h/C) = 2. 3 cycles , 

 for 27ra=406 Hz, fi = 1250 km, u = \ cm/sec, C=1.5 km/ 

 sec. As a model of coherent phase modulation, set 



TABLE V. Representative magnitudes in the Northwest Atlantic for the vertical displacement J and horizontal 

 velocity u of tides and internal waves at thermocline, sound channel and abyssal depths (/; = 0. 1 , 1 , 4 km). See 

 text. 



243 



