part of the mixed layer. Equation (2) is new equal to or nearly equal to 

 zero in the mixed layer: 



N o + \ + V + v = ° 



The fourth and perhaps the first terms continue to exist below the area 

 of interface. The term N Q is not completely equal to zero in the presence 

 of internal waves. Of the spectrum of orbital motions existing during 

 mixing, the portion due to internal waves remains and may interact with, 

 the horizontal flow in the thermocline, thus maintaining mixing in the 

 region of the interface. 



When the mixing process in the mixed layer ceases, the layer should 

 begin to decay immediately. The depth of the thermocline at any age should 

 be inversely proportional to the age r (in days), inversely proportional to 

 the mean horizontal velocity 7 in the thermocline, directly proportional to 

 the thickness h of the mixed layer at the steady state, and directly pro- 

 portional to the length L (in miles) of the mixed field. An expression for 

 thermocline depth h T at any age, combining all the involved factors, is: 



h T =^-hL (5) 



where K is a proportionality factor. 



K could be determined empirically, if the other five quantities in 

 Equation (5) were known or could be easily measured. However, usefulness 

 of this equation would be very limited, even if K could be determined. 

 Such a simple situation seldom occurs in the oceans. For example, if the 

 wind stopped abruptly over a fully developed sea which had previously been 

 subjected to a wind field of 30 knots and in which the thermocline depth 

 was in a steady state, aging of the mixed layer would begin as soon as the 

 sea surface became almost calm and the pure wind current had stopped com- 

 pletely. If the calm condition continued, Equation (5) would apply. 



As a second example, if a fully developed sea with given stability in 

 the thermocline and a wind field of 30 knots are assumed, the mixed layer 

 would maintain a thickness of 120 feet. Then suppose the wind field 

 diminishes to 20 knots and continues to blow indefinitely in the same 

 direction; the wind wave spectrum will gradually conform to the reduced 

 wind condition, and turbulence in the mixed layer will accordingly be 

 weaker; however, mixing will continue under neutral conditions to 120 

 feet. Under wind conditions of 30 knots, turbulence in the region of 

 the interface can penetrate no deeper, because it is arrested by thermo- 

 cline stability; but since the mixing reaches considerably deeper under 

 neutral or nearly neutral conditions and given wind conditions, turbu- 

 lence produced by a wind of 20 knots may be sufficient to. resist detrition 

 at the interface and deformation of the existing mixed layer to 120 feet. 

 In such circumstances decay would be prevented, and the mixed layer pre- 

 viously formed by turbulence caused by 30-knot winds would continue to 

 exist as long as the turbulence produced by weaker surface conditions was 



22 



