652 The Tropospheric Circulation 



To the Dynamics of UpweUing 



There are a number of causes for the vertical water movements in the ocean. For 

 continuity reasons these vertical motions are closely connected with the divergence 

 and convergence of the surface waters, and there is no doubt that the upwelling and 

 sinking of oceanic waters is primarily connected with convergence and divergence 

 regions occurring at the sea surface. The cause of these divergences and convergences 

 in most cases lies in the distribution of wind stress exerted by the prevailing wind on the 

 sea surface. A totally satisfying explanation of upwelling at continental coasts has not 

 yet been given, and is probably not possible at all since the total process is composed 

 of a number of substages each of which is always controlled by other factors. Coastal 

 upwelling is confined to a narrow strip close to the coast (less than 100 km) and must 

 therefore be regarded as a boundary phenomenon. 



It is a known fact that winds blowing at a suitable angle to a coast will carry light 

 surface waters away from it and the water mass transported away must be replaced 

 near the coast by heavier subsurface water. Defant (1952) gave a theoretical explana- 

 tion on the assumption of a sea composed of two layers with different density; previous 

 to this a more general investigation was made by Jeffreys on the effect of a steady wind 

 on the surface of a homogeneous ocean near the coast. The application of a theoretical 

 model as simple as this showed that the stationary wave disturbances at right angles 

 to the coast take their origin from the piling-up region or the upwelling region 

 ("Anstau oder Auftriebsgebiet") near the coast (see Fig. 306) and gave results in good 

 agreement with those obtained by observation. 



A theory of the upwelling produced by a wind parallel to a coast has been given 

 by HiDAKA (1954) whereby the effect of the earth's rotation and the frictional forces 

 due to both vertical and lateral mixing have been taken into account. He deals only 

 with a case of a steady state. The equations of motion, together with the equation of 

 continuity and the boundary conditions which must be satisfied at the sea surface and 

 along the coast, give a rather complicated solution to the problem. Calculation of the 

 magnitude of the off-shore currents and the upwelling velocity for a numerical 

 example allows the results to be compared with values estimated correctly from obser- 

 vations. Figure 307 gives the solution in the form of stream lines in a vertical plane 

 perpendicular to the coast. Upwelling develops close to the coast and there is no 

 off-shore movement of the water in the upper layers of the sea directly beneath the 

 surface swept by the wind. The upwelling is confined to the strip until 0-5Z)„ from the 

 coast and the sinking process occurs outside the wind zone. If the vertical mixing co- 

 efficient ^4^, is chosen with a value of about 1000 then the vertical Ekman frictional 

 depth Z)^, will be 162 m at 30° N. For a horizontal mixing coefficient A^ = 10^ the 

 horizontal frictional depth will be about 162 km. Estimation gives the width of the 

 coastal upwelling region as ID^ = 339 km. From this the average velocity between 

 the surface and the layer 0-2Z),, can be calculated as 3-35 cm/sec (off-shore the maxi- 

 mum upwelling is 2-7 m/day upward or approximately 80 m/month). Sverdrup 

 (1938) obtained a similar large value for the upwelling velocity off southern California. 

 The depth at which the upwelled water originates is about 200 m which is also in fair 

 agreement with observed values off the southern Californian coast. Hidaka has also 

 investigated the cases arising when the wind is at certain angles to the coast. If the 

 wind is at right angles to the coast, then the induced circulation has a rather complicated 



