Z,E,E 



summation over ray path /, internal wave mode ;', ray loop k 



(;-'>= 0.435 

 F{^,i;z), G{oj), H(j) 

 Ejw), £:,(co) 

 a),„ = 7.3xl0'^ sec'' 



(Ii = a)/2;r, h = n/2Ti, etc. 



A =ritane/a),„ 

 a, y, 13 = ay 



Eq. (90), usually ;^ =3 



Eq. (95) for ;^ =3 



internal wave spectra 



acoustic phase and intensity spectra 



inertial frequency at 30° latitude 



frequency limit 



cyclical frequencies (usually in cycles per hour, cph) 



Eq. (99) 



Eq. (107) 



Eq. (109) 



Eqs. (96), (98), (102), (104) 



INTRODUCTION 



Sound scintillations in the sea may be regarded as the 

 result of weak scattering. The fluctuations in sound 

 velocity are small, typically 6C/C = 5xl0'* in the upper 

 layers, 3x10'° at abyssal depths. But the range of 

 propagation can be very long, and the cumulative effect 

 pronounced. The fluctuations impose the ultimate limit 

 to the acoustic resolution of objects, similar to the 

 resolution limit of ground-based telescopes due to 

 "atmospheric seeing." 



Our purpose is to contribute toward a quantitative 

 connection between two observational programs that 

 have paid scant and reluctant attention to one another. 

 Measurements and analysis of the fluctuating sound 

 transmission have viewed the ocean as a transmission 

 channel and described its properties by certain corre- 

 lation functions that are not readily identified with known 

 physical processes. Oceanographers have studied 

 ocean variability with emphasis on the associated fluxes 

 of momentum, energy, salt, etc. Starting from an 

 idealized (but not absurd) model of ocean variability, our 

 goal is to compute certain quantities of experimental in- 

 terest, such as the mean square phase and intensity 

 fluctuations of received sound pressure, and to compare 

 these with measured values. 



The procedure is to derive a formalism for which 

 the geometric optics limit valid for short ranges is 

 transparent, and the transition to larger ranges is easi- 

 ly visualized. Section I gives the solution for a homo- 

 geneous ocean, with the geometric optics limit subject 

 to a Fresnel condition [Eqs. (35) and (39)|. But the 

 real ocean is not homogeneous, nor is it isotropic. In 

 Sees. II and III the solutions are generalized to apply to 

 an inhomogeneous ocean [Eqs. (57) and (62)] and to the 

 special case of a vertically channeled ocean [Eqs. (66) 

 and (76)], respectively. The range of validity of geo- 

 metric optics is now actually extended, and in addition 

 we are able to obtain rather simple analytic expres- 

 sions for quantities of experimental interest both within 



and beyond the geometric optics regime. 



We next introduce a specific gross sound velocity 

 profile C(z) with perturbation 6C due to vertical strain- 

 ing of the gross structure from internal wave activity: 



C(x, y, z, t) = C{z) + 5C{x, y,z,t) + --- . 



The effect of horizontal flow associated with internal 

 waves is smaller than that of vertical straining. We 

 also ignore intrusive and other forms of fine structure 

 which, apart from their intrinsic temporal evolution, 

 are carried around by currents and internal wave mo- 

 tion. 



There are two immediate questions: are internal 

 waves and internal tides (in constast to turbulence, 

 planetary waves, . . . ) the principal source of fluctua- 

 tions? Do we have an adequate statistical model of 

 internal wave activity? 



To the first question the answer is yes within a fre- 

 quency interval between cycles per day and cycles per 

 hour. Vertical displacements by internal waves are 

 typically tens of meters and swamp other sources of 

 fluctuations. The oceanographically more important 

 planetary waves (related to the variability in ocean cur- 

 rents) are associated predominantly with horizontal dis- 

 placements and are therefore of less consequence to the 

 sound field; their frequency range is typically cycles 

 per month to cycles per week. But in special frontal 

 zones (e.g., near the Gulf Stream) the long-period 

 changes in sound transmission are probably planetary 

 wave related. Small-scale turbulence takes over below 

 the Richardson length' (€/«')' '^ = order (1 m). But for 

 intermediary scales the buoyancy effects are predomi- 

 nant and the fluctuations are internal wave related. 

 Reliance on laboratory concepts of homogeneous iso- 

 tropic turbulence, though fashionable, seem to us to be 

 entirely misplaced. 



The answer to the second question is no. We shall 

 apply the internal wave models by Garrett and Munk 



213 



