. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 24 MECHANISMS FOR STEADY SHELF CIRCULATION bu_ bz~ = A, b3v bz3 0 = bit bs u — h w Ox bz bw bz = A', bz2 (2) (3) (4) For this right-handed coordinate system, x is perpen- dicular to the coast, v is parallel to it, and z is vertically upward; ;/, r, w are the v. r, Z components of velocity, respectively; .1, and A, are the vertical eddy mixing coeilicients for momentum and salt; s is the salinity; and 0 is the coefficient of contraction for salt. The
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography 24 MECHANISMS FOR STEADY SHELF CIRCULATION bu_ bz~ = A, b3v bz3 0 = bit bs u — h w Ox bz bw bz = A', bz2 (2) (3) (4) For this right-handed coordinate system, x is perpen- dicular to the coast, v is parallel to it, and z is vertically upward; ;/, r, w are the v. r, Z components of velocity, respectively; .1, and A, are the vertical eddy mixing coeilicients for momentum and salt; s is the salinity; and 0 is the coefficient of contraction for salt. The effects of the earth's rotation are contained in the terms fv2 and ///-, where / is known as the C'oriolis parameter and / = 20 sin 8 where it is the angular velocity of the earth and 6 is the latitude. To arrive at these equations it is assumed that the effects of lateral mixing are small, and that the motions are slow and steady so that nonlinear effects and time dependence can be neglected. To simplify the problem further it is assumed that the motion does not vary in the direction parallel to the coast, , d( ) by = 0. The geometry is shown in Fig. 1. At the coast there is a laterally distributed transport of fresh water (river runoff) denoted by Tr. This sets up a salinity gradient normal to the coast. What arc the implications of this gradient? Equation 1 is where ( h dc ~f1'' = —gP** + Asu„, ( ), ( )„ = d- ( ), In an estuary where there are lateral side walls, o is either very small or absent. Similarly, on the shelf it can be shown that in shallow' water, or for large values of A, and A',., this is also true. In such situations the term fv2 can be neglected and vuzzz - g(3sx. U :m/sec 0 2 0 1 1 1 1 1 V 1 .8 / -2/h .A ..2 FIGURE 2. Vertical profile of the offshore velocity for the fol- lowing parameters: Av = 102 sec'1; g/3sx = X 10~s; H = 5 X 10 cm; TK = 50 cm2/sec. Situations exist on the shelf or in estuaries in which sx is essentially i
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