Spatial Correlation of Ocean Movements and Sound-Velocity Fluctuations
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FIG. 3. Dimensionless residual stress for r >a/c.
FXG. 4. Dimensionless velocity for r =a/2c; at t =ia/c.
3. Relaxation Interval (r
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FT. 1. Comparison of sound-velocity variations measured at a depth of 560 m (solid curve) at a location near Bermuda with the to-and-fro movements of a ship located 71 km to the southwest (dashed curve). Calculated variances of the series were used to adjust the scales.
In the present experiment, the source was not rigidly fixed in position, so that one could expect both internal waves and source motion to influence the fluctuations of the acoustical signal. This circumstance makes cross correlation between acoustical fluctua-
tions and internal wave motions difficult. Nevertheless, correla- tion exists between the ocean movements at the two ship locations during the experiment that may help to explain the acoustical observations under analysis.
Sequentially raising and lowering a sound velocimenter and a depth sensor permitted a sound-velocity measurement nearly every 6 min throughout the interval of 50 to 650 m. The water was nearly isothermal between 200 and 450 m. Figure 1 shows in solid curve the sound velocity variations for the depth of 560 m. This depth is just below the knee of the isothermal layer in the main thermocline: An increase in the sound velocity corresponds to a descent of the water. The oscillations of the interface of a two-
layer ocean can be shown to be more peaked in the direction into the thicker layer, in this case, downward. This seems to be the circumstance suggested by the sound velocity fluctuation data since these fluctuations are more often peaked when sound velocity increases.
The dashed curve superimposed on the solid curve with a time lag of 4 h for maximum correlation represents the to-and-fro movements of the source ship located 71 km away from R/V CHAIN where the sound-velocity measurements were made. The cross-correlation function in Fig. 2 is not symmetric and indicates maximum correlation occurring at 4-h time lag.
The depth variation of the 21C isotherm between 55 and 90 m as measured from a series of bathythermographs from the source ship also shows a correlation with the sound velocity fluctuations measured from R/V CHAIN, with about a 5-h time lag.
The lag in the correlation might be explained by internal tidal waves in the open ocean. The semidiurnal tidal period of 12.42 h has been observed in current measurements from deep moorings. a However, the time series in the present experiment was not long
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FIG. 2. Cross-correlation of the sound-velocity time series and the time series of the ship position.
enough to permit calculation of the period of the wave. If an internal tidal wave was present it would tend to propagate toward the east for the location of the experiment at the internal gravity wave speed of 4 m/sec. This speed corresponds to (Ap/p)gh, where p/p is the relative density change, g is acceleration of gravity and h the interface depth, under the assumption of a two layer ocean model. The parameters Ap/p = 2X 10% h--800 m are chosen appropriate to the Sargasso Sea where the water depth is 5 km. A wave propagating at this speed would cover a distance of 54 km in about 4 h. This distance is the
east-west component of the separation of the two ships. The internal tidal-wave length is very long as compared to the
layer thickness and water depth, and therefore ship movements ought to be influenced by these wavesJ The speed of the water movement at the sea surface can be estimated to be 0.04 m/sec. from [(Ap/p)g(a'/h), where a is the amplitude of the interface wave for a two-layer ocean model. An interface amplitude of 8 m was estimated from the maximum sound-velocity variation (solid curve in Fig. 1) and the sound-velocity gradient of m/sec. The calculated flow speed at the sea surface is close to the speeds observed from the slopes of the dashed curve for ship motion.
Acknowledgment' This work was supported by the Office of Naval Research.
* Contribution No. 2276 from the Woods Hole Oceanogr. Inst. The acoustical measurements were undertaken in a joint research
program with members of the Bell Telephone Labs. J. C. Beckerie, J. L. Wagar, and R. D. Worley, "Underwater Acoustic
Wavefront Variations and Internal Waves," J. Acoust. Soc. Amer. 44, 295-296 (1968).
a F. Webster, Progr. Oceangr. (Pergamon Press, New York, 1968) Vol. 5. a H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge,
England, 6th ed. (1932), Chap. IX, Art. 231.
Received 9 December 1968 13.3; 11.3
Comments Concerning the Determination of Ab- solute Sound Speeds in Distilled and Seawater and Pacific Sofar Speeds
J. R. LOVETT Naval Undersea Warfare Center, San Diego, California 92132
The preponderance of recent determinations of distilled-water sound speed indicates that the Wilson (for the range 0-30C) and Greenspan-Tschiegg sound-speed equations are too high by 65 and 40 cm/sec, respectively. Similarly, the Wilson seawater sound-speed equation gives Pacific temperate latitude Sofar speeds - m/set higher than values based on explosion travel times. Adjusted distilled and seawater equations are proposed in order to achieve a common standard for all measurements at sea.
FOR THE TEMPERATURE RANGE 0-30C, THE WILSON 1 DISTILLED- water equation is too high by about ] m/sec when it is compared and 10 with recent determinations -11 of distilled-water sound
speed. If one assumes the criterion that the speed of sound changes
smoothly with temperature and that the sound-speed derivative decreases monotonically as temperature increases, then aside from
The Journal of the Acoustical Society of America 1051
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