SECT. 3] DYNAMICS OF OCEAN CURRENTS 379 



Lo = 2\Woo\holWe -0.78 



Ao = \Wo.\%olkv{2We+\Wa,\) -0.29 



hi = 2kvlWeho -1.14 



A2= (- 



PFe 



0.69. 



The magnitudes of the constants and the approximate solutions of (210) and 

 (211) are given for the values: We = ^ Dcm sec~i, Woo= —2 Dcm sec~i qo* = 

 30 D°C cm sec-i and kv = l cm^ sec-i, where D indicates the dimensions, 

 (°C cm sec)'/3, of (a:/e)'/3. For (x/e)^3-7x lO^D, or a; - 4500 km and e-1.3x 10-6 

 °C-i sec-i, these values correspond to vertical velocities of + 2.9 x 10"^ cm sec^i 

 in the deep water and — 4.3 x 10"^ cm sec-i at the bottom of the Ekman layer 

 and a heat flux of 4.3 x 10-^ cal cm-2 sec-^. For these values, which may be 

 considered typical of real oceans, the surface of zero vertical flow is at 320 m 

 and the depth interval corresponding to L is 920 m. The vertical range of 

 temperature is 30.6°C and the meridional gradient is — 4.3°C per 1000 km. 

 The model is very sensitive to the value assumed for kv. For example, if we use 

 kv = 2 cm2 sec-i, the vertical temperature range is reduced nearly in half to 

 16.5°C, the depth of the upper layer is increased to 570 m and L to nearly 

 1300 m. The meridional gradient, however, is increased only to — 4.5°C per 

 1000 km. An increase in the vertical velocity of the deep water reduces both h 

 and L and the meridional gradient of temperature but increases the surface 

 temperature. 



At a given position in the ocean, there are nine variable parameters required 

 to describe the model: We, qo*, ^o, Ti at ^ = 0, qn*, ^h at <^ = h, the two charac- 

 teristic depths, h and L, and the deep-water velocity, Woo. In addition, the eddy 

 diffusivity, ky, is unknown and must be treated as a variable parameter. There 

 are six relations among the total of ten parameters. In principle, we can choose 

 any four of the parameters independently and solve the equations for the 

 remaining six. Thus, we can apply the model to the real oceans by evaluating 

 from observations four of the more readily observable parameters and using 

 the model to obtain estimates of the remaining six. Robinson and Stommel, 

 for example, evaluated We, &h, h and L from observations and used relations 

 similar to (204) to (209) to estimate Woo, &o and kv. Additional parameters that 

 can be estimated from observations can be used to check the consistency of the 

 model. 



The upward flow from the deep water is arbitrary from the point of view of 

 the thermal mechanism except that it cannot be zero in regions where the 

 Ekman transport is convergent. As the major part of the world ocean is covered 

 by a convergent Ekman layer, the total upward transport can be comparable 

 to the transports of the horizontal flows. Stommel and Arons (1960a) estimate 

 the total upward transport to be of the order of 40-50 million cubic metres per 

 second. The deep water lost through the thermocline is presumably replaced in 

 relatively concentrated regions of sinking in the North Atlantic Ocean and the 



