Dynamics of Coastal Models - Manejo Costero

308 Advection of momentumbasin, is the ratio of the inertial term to the bottom friction stress. Noting that (8.50)and (8.51) giveu @u@x ¼@HgF2@xthe Reynolds number is defined in terms of h and C d as(8:53)R hu@u=@x j jC d u 2¼ @h=@xC d(8:54)and our interest lies in h increasing with x (Figure 8.9). Hence, using (8.49)to(8.52) thesteady state dynamic equation (8.48) becomes, for positive u,When R < 1,R518 1, the surface elevation increaseswith x, producing a pressure force that acts in the same direction as friction to opposethe advective terms. When R > 1, and the current is again positive, (8.55) shows thatR418 1, the bottom slope is supercritical and otherwise subcritical.Hence, any attempt to drive a current down a supercritical slope with a surfaceelevation that decreases in the direction of the current will produce a supercriticalflow; to obtain subcritical flow, the elevation must increase with x.8.4.3 Model of flow down a slopeThe theoretical development will consider the simplest possible coastal basin in whichthe bottom slope (and hence R) is independent of x (see Figure 8.9). The variation of H