General Theory of Ocean Currents in a Homogeneous Sea 437 



a resisting force arising from the random movement of the ice which is proportional to 

 the drift velocity and acts in the opposite direction. This ice resistance is the reason why 

 the Ekman theory for the ice drift is inadequate. Nansen had already shown in 1902 

 from the "Fram" data that the ice resistance cannot be neglected and indicated that one 

 of its effects must be the small deflection angle observed for the ice drift. Brennecke 

 (1921) and Sverdrup (1928) have made important contributions to the clarification of 

 the interrelated forces acting and that of Sverdrup can be regarded as a complete 

 theory of the ice drift (see also, Rossby and Montgomery, 1935). However, the 

 observations of the "Fram" are not suitable for testing this theory, since the ice drift 

 here includes a component due to the permanent surface current (see p. 358), but over 

 the North Siberian Shelf ("Maud" observations) and in the Weddell Sea ("Deutsch- 

 land" observations) the ice drift is free from a basic current and is suitable for this pur- 

 pose. There is, however, one fundamental difference between these two drifts, due to the 

 very different hydrographic conditions under which these drifts occur, and this has a 

 considerable effect on the nature of the pure drift current (without ice). 



Over the Siberian Continental Shelf the oceanic structure consists of essentially 

 two layers: a top layer of lighter water and a heavier bottom layer separated by a 

 sharp density transition layer (thermocline). In the surface layer the vertical equili- 

 brium state is indifferent (neutral) throughout almost all the year and the turbulence 

 in it is intense. In the discontinuity layer it falls nearly to zero and this therefore has 

 the character of a gliding layer. The entire water mass of the top layer is thus drawn 

 along with the surface current and this, together with the ice masses floating in it, 

 behaves like an elastic sheet. The resistance against the movement thus arises from 

 the effect of varying winds driving this sheet together. In the deep Weddell Sea the 

 oceanographic conditions are different; here there exists no transition layer near to 

 the sea surface and the density increases continuously with depth. A drift current thus 

 develops in the normal way, and also the expected decrease in the velocity of the current 

 and its turn in direction could be observed. In the Weddell Sea it appears necessary to 

 take into account the effect of turbulent friction besides that of the ice resistance. 

 These circumstances require to deal with each of the cases separately. 



A shallow sea with a density transition layer (thermocline). The wind stress is taken as 

 proportional to the wind velocity u' and thus as equal to cw (c is termed the wind 

 effect); the resisting force (ice resistance) as proportional to the velocity of the ice 

 drift and in opposite direction of it is denoted by —ku (with components — A:m^ and 

 —kUy along the co-ordinate axes). Then as shown by Sverdrup for the case of the 

 North Siberian Shelf, for non-accelerated motions (wind along the positive j-axis) 



This gives 



where 



(XIII.60) 



tan a = — , „,,v. , — — y.-^ 

 Uy k vv / 



