The calculated wind stress is applied directly 

 to the mixed layer, since it has been shown 

 (Richman and Garrett, 1977) that 97% of the 

 momentum input to the surface is transmitted 

 eventually to the mixed layer. If a more substan- 

 tial portion of the wind energy had been advected 

 away by surface waves, the wind stress into the 

 mixed layer would have to be reduced by some 

 factor. 



Equations 1.11 through 1.14 were solved nu- 

 merically at each time step, as analytical solu- 

 tions are not possible. 



2. Mixed Layer Deepening and Thermocline 

 Changes. 



An important construct in the motion equa- 

 tions is the mixed layer depth D. When the wind 

 forces the mixed layer into motion, the magni- 

 tude of this forcing function is determined by 

 both the magnitude of the wind stress and the 

 depth of the mixed layer, because of the applica- 

 tion of the wind stress as a body force. 



It is important to include not only deepening of 

 the layer due to unstable internal waves at the 

 interface of the moving water and the stable fluid 

 below (Pollard, Rhines and Thompson, 1973), but 

 also the possibility of the formation of a shallow 

 lens of warmer water near the surface due to low 



mixing by the wind and high solar radiation. 

 This shallower layer of warm water would then 

 become the layer acted on by the wind stress, 

 because the density gradient caused by tempera- 

 ture at its base would then be the barrier to the 

 penetration of the wind's energy. 



Figure 2.1 illustrates this phenomenon. 2.1(a) 

 is at the conclusion of some wind event, with a 

 fully developed mixed layer. 2.1(b) is at some 

 time later than (a). In the interim, there has been 

 a period of relative calm, with solar heating, D^, 

 the new mixed layer depth is much less than D^, 

 the previous depth. At some new wind event, the 

 controlling depth for the calculations would be 

 Dg, because of the thermal gradient at z=D,. At 

 this new wind event, the old motions of the water 

 below the new mixed layer depth D^ would con- 

 tinue unforced because the wind energy would be 

 limited in its penetration into the water by the 

 temperature and density gradient at z=D^. Veloc- 

 ity shears can therefore occur at the boundary 

 between the new and old mixed layers, at depth 

 D,. These velocity shears may be responsible for 

 observations in the deep oceans of structures 

 interpreted as Ekman spirals (Assaf, Gerard and 

 Gordon, 1971). 



r »o 



T— ° 



Figure 2.1 Schematic or the Formation of a New, Shallow Mixed Laver by Low Winds and Insolation. 



4 



