S ic, ,e,v) = (ag2/a;5) [exp - /3 (%/w ) ^ ] F (co, ^*, v ) m2s 



where: a = 8.1 x 10"^ m^/s, (3 =0.74 and % = g/^i9.5> rad/sec 



*'l9.5 is the wind speed at 19.5 meters above the sea surface, 

 and F (co, 6*, v ) is the beamwidth of the wave spectra depending on wave 

 angular frequency (w), wind speed (v) , and direction (^*) measured with 

 respect to direction of the wind and is between +7r/2. For the fully 

 risen or equilibrium sea, this spectrum falls off as w -5 . The exponential 

 term gives growth portion of the curve. 



c. The Thermocline and Internal Waves 



Fluctuations, variations, and waves in the temperature 

 structure of the thermocline occur quite frequently in the ocean and 

 can have important consequences for duct propagation. The sharp density 

 gradients of the thermocline give rise to gravity oscillations, called 

 internal waves (fig. 6-9). Oceanic internal waves generally have wave- 

 lengths, periods, and amplitudes much larger than surface waves. Internal 

 waves travel much slower than surface waves. These waves may have 

 periods measured in minutes and hours, wavelengths in kilometers, and 

 amplitudes of the order of tens of meters. 



There are theoretical maximum and minimum frequencies for free 

 internal waves. The theoretical maximum frequency is known as the 

 Vaisala frequency. The theoretical lower limit is defined by the 

 Coriolis parameter. The Vaisala frequency N is expressed in terms of 

 density p , density gradient dp/dz, gravity g, and sound speed C, in 

 the medium as follows: 



■^ ^ ^ P 6z a' 



The maximum frequency is a function of depth; it is largest in the 

 thermocline and least at depth of weakest density gradient. A contin- 

 uous monotonically decreasing power spectrum seems to exist between 

 minimum and maximum frequencies along with line frequencies of internal 

 waves. 



Several different types of forces have been identified as 

 causing internal waves. Tidal and other forces that impel water 

 movement around land boundaries and topographic features can start 

 oscillations in the thermal structure. Strong winds may create 

 convection cells and eddies in the upper layers of the sea, and the 

 resulting circulation will cause current shears and waves on the 

 thermocline. Vertical oscillations in the thermocline can be induced 

 by air pressure changes and fluctuating winds at the sea surface. 

 Currents crossing sills or underwater mountain ranges may lead to 

 internal waves. 



Power spectra of internal waves seem to show regions of distinct 

 frequency behavior (fig. 6-10). Power spectra show that the greatest 



21 



