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where a is the absorption coefficient (dBkm ) and f the frequency (kHz). The factor 1.0936 converts the original formula from units of dBkyd to dBkm . More recent formulae for the absorption coefficient have been described by Fisher and Simmons (1977) and by Francois and Garrison (1982a,b). Ainslie and McColm (1998) simplified a version of the Francois-Garrison equations for viscous and chemical absorption in sea water by making explicit the relationships among acoustic frequency, depth, sea-water absorption, pH, temperature and salinity. An older dataset that has received renewed attention is that reported by Skretting and Leroy (1971), which included measurements of sound attenuation in the western Mediterranean Sea.

In practice, the effects of absorption and attenuation are considered jointly. Then, the frequency dependence can conveniently be segregated into four distinct frequency regions over which the controlling mechanisms can be readily identified. These regions are (in order of ascending frequency): (1) large-scale scattering or leakage; (2) boric acid relaxation; (3) magnesium sulfate relaxation; and (4) viscosity. Fisher and Simmons (1977) summarized these effects graphically (Figure 3.14). Research conducted by

Figure 3.14 Absorption coefficients for sea water at a temperature of 4°C at the sea surface. Dashed lines indicate contributing absorption rates due to relaxation processes (Fisher and Simmons, 1977).

other investigators provides regional formulae for absorption and attenuation (Skretting and Leroy, 1971; Kibblewhite et al., 1976; Mellen et al., 1987a-c; Richards, 1998). Absorption is regionally dependent mainly due to the pH dependence of the boric acid relaxation. Attenuation due to turbidity and bubbles was discussed in Section 3.4.3.

The Applied Physics Laboratory, University of Washington (1994), documented high-frequency (approximately 10-100 kHz) acoustic models with potential application to sonar simulation and sonar system design efforts. These models treat volumetric sound speed, absorption and backscattering; boundary backscatter and forward loss for the sea surface and the sea floor; ambient-noise sources and levels and Arctic attenuation and under-ice losses.

3.7 Surface ducts

Sound travels to long distances in the ocean by various forms of ducted propagation. When sound travels in a duct, it is prevented from spreading in depth and remains confined between the boundaries of the duct. The surface duct is a zone bounded above by the sea surface and below by the SLD. Within the surface duct, sound rays are alternatively refracted and reflected. A surface duct exists when the negative temperature gradient within it does not exceed a value determined by the effect of pressure on sound speed (refer to Chapter 2). Specifically, the surface duct is characterized by a positive sound-speed gradient. For example, in isothermal water (and ignoring the effects of salinity), the pressure effect will produce a positive sound-speed gradient of 0.017 s-1.

The surface duct is the acoustical equivalent of the oceanographic mixed layer, although they are defined differently. While the SLD is normally defined in terms of the sound-speed gradient, the MLD is defined in terms of temperature, or more precisely, in terms of density (which is a function of temperature, salinity and pressure). The mixed layer is a quasi-isothermal layer of water created by wind-wave action and thermohaline convection. Algorithms for the prediction of surface duct propagation will be discussed in Chapter 5. These algorithms use the depth of the mixed layer as an input variable.

3.7.1 Mixed-layer distribution

Oceanographers have extensively studied the dynamics of the mixed layer. Variations in the temperature and depth of the mixed layer are closely related to the exchange of heat and mass across the air-sea interface and are thus of interest to scientists engaged in studies of the global climate. Lamb (1984) presented bimonthly charts of the mean mixed layer depths for the North and tropical Atlantic oceans. Bathen (1972) presented monthly charts of MLDs for the North Pacific Ocean.

Figure 3.15 Mixed layer depths (m) for March based on (a) a temperature criterion of 0.5°C and (b) a density criterion of 0.125 x 10-3gcm-3 (Levitus, 1982).

Levitus (1982) presented charts of MLDs on a global basis. Distributions of MLDs were calculated using both a temperature criterion and a density criterion. The temperature criterion was based on a temperature difference of 0.5°C between the surface and the depth referred to as the MLD. The density criterion was based on a difference of 0.125 x 10-3 gcm-3 between the surface and the depth of the mixed layer. The use of the density criterion recognized the importance of salinity in determining the stability of the mixed layer and hence, from an acoustics viewpoint, the true depth of the sonic layer. For example, in sub-arctic regions, isothermal conditions (or even temperature profiles with inversions) combine with a salinity profile that stabilizes the water column to control the depth of mixing. Mixed layer depths for the months of March and September are presented in Figures 3.15 and 3.16, respectively, comparing the global distributions resulting from both the temperature and the density criteria.

0° 30° E 60° 90° 120° 150° E 180° 150° W 120° 90° 60° 30° W 0°

Figure 3.16 Mixed layer depths (m) for September based on (a) a temperature criterion of 0.5°C and (b) a density criterion of 0.125 x 10-3 g cm-3 (Levitus, 1982).

0° 30° E 60° 90° 120° 150° E 180° 150° W 120° 90° 60° 30° W 0°

Figure 3.16 Mixed layer depths (m) for September based on (a) a temperature criterion of 0.5°C and (b) a density criterion of 0.125 x 10-3 g cm-3 (Levitus, 1982).

Traditionally, it has been assumed that the mixed layer is the vertical extent of the turbulent boundary layer. Peters and Gregg (1987) have pointed out that the turbulence initiated by the exchanges of energy, buoyancy or momentum across the air-sea interface may actually penetrate the lower boundary of the mixed layer as defined by the previous criteria. Thus, precise discussions of the mixed layer are often frustrated by imprecise terminology.

Some regional examples will serve to clarify features of the mixed layer as evidenced by the thermal structure of the water column. For these examples, the continental shelf region off the Texas-Louisiana coast in the Gulf of Mexico (Etter and Cochrane, 1975) will be explored. Figure 3.17 presents the annual variation of water temperature down to 225 m. In this graphical representation, the seasonal variation of the depth of the mixed layer is portrayed as a uniform layer of temperature versus depth. In January,

Month

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