558 EIGHTH PACIFIC SCIENCE CONGRESS 



consideration. And it may be stressed that the horizontal mixing seems^ 

 to play the most important role in the theoretical explanation of the 

 process of upwelling. 



2. Theory 



Consider an infinitely long straight coast coincident with the axis of 

 y, and take x-axis perpendicular to it in the offshore direction. (Fig. 1). 

 Suppose a wind of constant force and direction is blowing steadily and 

 uniformly in a belt of limited width L parallel to the coast from nega- 

 tive to positive direction of }'. This is a disposition favorable for the 

 upwelling to actually occur. Take the z-axis vertically downwards. 



In a steady state which is attained after a sufficiently long time since 

 the wind began to blow constantly, the motion of water will be inde- 

 pendent of y. This means that all the vertical and horizontal compo- 

 nents of the currents can be determined as functions of x and z only. 

 Moreover, the surface of the sea will not be a plane, but have a slope 

 in the x-direction. In such a case, the hydrodynamical equations of 

 motion of sea water are, after several reasonable simplifications, 



H i- 2(0 sin (j)V — g-^^ — = 



P 9x2 p 9^2 "ax 



A^ d'v A^ d^ ^ . 



-i 2o) sm (hu = 



where u and v are the horizontal components of the current velocity 

 in the x and y directions, ^ the surface elevation depending on x only, 

 P the density, A^ and A^^ the coefficients of vertical and horizontal mix- 

 ing, of sea water, « the angular velosity of the Earth and ^ the geographic 

 latitude. In addition to these, ^ve have the equation of continuity in 

 the form: 



^" + -^ = (2) 



3x dz 



where w is the vertical component of currents and represents the intensity 

 of the upwelling, and because dvjdy = 0. 



Suppose the wind blows in the positive direction of }> in a belt 

 between the coast x = and x = L. The wind velocity may vary in 

 the offshore or x-direction. The conditions to be satisfied on the sur- 

 face of the sea are therefore at 



"^'dz -^ (3> 



0: 



— = T forO ^^^ L 



dz 



= f or L < X < 00 



