Effect of Wind on the Mass Field and on the Density Current 547 



of the physical sea level in the ratio Pi:(p2 — Pi). It is easily shown that this slope is 

 given by 



•_ ^ 



g{p2. — Pi)hi 



where pi and p, are the densities of the top and lower layers, respectively, h^ is the thick- 

 ness of the top layer when the system is at rest and T is the shearing stress of the wind. 

 The deep water is assumed to be motionless. This relationship has the same form as 

 the equation (XIII.45) which gives the piling up of water by the wind (Windstau) in a 

 homogeneous sea except that p is replaced by the density difference (pa — pi). 

 Hellstrom (1941) showed that in a stratified sea with two layers the piling up of 

 water by the wind differs markedly from that in homogeneous water and that the effect 

 of the wind is larger. The wind stress calculated from equation (XIII.45) (p. 419) is 

 much too large, and the less the depth of the discontinuity layer the greater is the error. 

 Palmen's investigations, however, showed that the changes in water level in the Baltic 

 due to the effect of the wind are almost independent of the water stratification. This 

 contradiction was resolved by Palmen (1941) by estimation of the time required to 

 establish an equilibrium state. This time required is very large, of the order of several 

 days, while only a few hours are needed to produce a piling up of the water similar 

 to that for homogeneous water. Usually, the wind direction does not remain invariable 

 for a longer time to allow the slopes of the discontinuity layer and the sea surface to 

 reach a steady state. Initially, the piling up of water by the wind in a stratified sea is 

 approximately the same as in a homogeneous sea. However, the longer the duration of 

 the wind the closer is the approach to the Hellstrom values. The equation (XIII.45) can 

 thus be used in almost all cases for the calculation of the wind pressure, although 

 strictly it is valid only for homogeneous water. 



Fjelstad (1946) has made a thorough theoretical examination of steady currents 

 in a stratified water contained in a wide channel and has obtained results in complete 

 agreement with the observations. 



The transverse circulation is usually connected with another important pheno- 

 menon. In a sea of sufficient width a strong wind may produce an inclination of the 

 density transition layer sufficient to bring the deep water to the sea surface. A rapid 

 fall in temperature will then occur and an increase in salinity in a long band along the 

 coast to the left of the current (Northern Hemisphere). The phenomenon of "cold 

 upwelling water" along an extended coastline has previously been regarded largely as a 

 direct result of an offshore wind (land wind) (Sandstrqm, 1922; Krummel, 1911, 

 p. 536 and following), forcing the deep water upwards to the surface at the lee coast 

 while the surface water is forced downwards to deeper layers at the windward coast (luv- 

 coast). Besides this direct effect, the effect of earth rotation in the above senses, seem 

 however, of more importance. In the Gulf of Finland and in the Baltic (Mae, 1928) the 

 upwelling of cold water found during strong persistent longitudinal winds gives 

 support to the importance of the indirect wind effect, 



2. General Conditions in the Open Ocean 



These are essentially the same as in channel-form elongated oceanic regions. The 

 efiFect of the wind is mostly restricted to a more or less broad band of the sea surface, 

 and outside this area the water is either motionless or subject to the effect of a wind 



