t - Comisión Interamericana del Atún Tropical

CURRENTS IN P ANAMA BAY409Here the depth-mean values of the velocity components were written because,since the pressure gradient is uniform with respect to depth, thecomponents of velocity must be also. For a net current of about 1.0 m/sec,which is stronger than any observed in Panama Bay, the correspondingslope of the sea surface is only 2.3 X 10- 6 • The minimum slope of the bottom,measured normal to the observed net flows, is about 10- 3 • Then, (x, y) can be neglected in the equation of continuity so that (4) becomeso - 0­oxayO == - (hu) + -- (hv) (6)When the expressions for the depth-mean components of velocity derivablefrom (5) are substituted into this and the variation of Coriolis force withlatitude is neglected then, as is demonstrated by Lamb (1932, Art. 207),the result iso, oh o, ohO == -- .~ 0- ~- -- (7)ox ay ay oxThis condition is satisfied only if the contour lines of the sea surface areeverywhere parallel to the bottom contours. In turn, because the flow isparallel to the contours of the sea surface, it must be parallel to the bottomcontours. However, this is arbitrary to the degree that there are twopossible directions of flow. Suppose for example that the bottom shoalsonly northward. Then (7) is satisfied if sea level rises or falls, or alternatelyrises and falls, in the same direction and therefore at any positioneither eastward or westward current is possible. Which direction the currentwould assume at any particular location requires prior knowledgeof the slope of the sea surface there.In the development just completed the influence of friction was neglected.Now this will be included but for the special case in which thereis generally westward flow parallel to a straight zonal coast with land tothe north and water to the south. If the hypothetical coast encircles theworld at its particular latitude then the equatio11 of continuity (6) is satisfiedeverywhere only if v is zero because there can be no depth-mean flownormal to the coast. When the frictional forces are included equations(5) becomeOo, + K 02VO = -fu - ga¡ p 3Z2(8)where K, the vertical coefficient of eddy viscosity, is assumed to be constant.When the first of these is integrated with respect to depth and thecondition v == O is imposed, then the result is