t - Comisión Interamericana del Atún Tropical

CURRENTS IN PANAMA BAY407t (x, y, t)h(x, y)pDeparture of sea level (m) from z == ODepth to bottom (m) measured from z == OWater density, assumed uniformg Acceleration of gravity, 9.8 m/sec 2fCoriolis parameter, 2.23 X 10- 5 /sec in Panama Bay, assumedconstantThe origin of time is taken to be simultaneous with a low water atBalboa.For most discussions it was convenient to make use of the horizontalcomponents of the depth-mean current which are defined as_ 1 r t (x, y, t)u(x, y, t) ==, + h J-h(x, y)u d z1 r t (x, y, t)v(x, y, t) = , + h J vd z-h(x, y)The form of the equations of motion used to discuss each characteristicof the currents usually is different for each problem and therefore eachis given below in the appropriate place. For all cases, however, the equationof continuity had to be satisfied and it was used in an integratedformo For water of uniform density the equation of continuity for anelement of volume isOU OV ow3X (x, y, z, t) + ay (x, y, z, t) + az (x, y, z, t) == OIntegration of this from the bottom to the sea surface, transformationaccording to Leibniz's rule (Osgood 1935), and substitution of (1) yieldso - o .- o,ax [(t + h)u] + ay [(t + h)v] = -31 (2)Integration of the differential form of the hydrostatic equation fromany depth z to the sea surface givesp(,) - P(z) == pg(z - ')If the sea level pressure p(') is assumed to be constant then, becausedensity is uniform, the components of the horizontal pressure gradientforce at any depth z are1 op(z)_ ot g_--=:­p ax-- 'Ox(1)