. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography EQUATIONS OF MOTION 57 60° - 58° 56° - 54° - 52° - 50°. FIGURE 4. Amphidromic systems of the Mj tidal constituent (semidaily lunar tide) in the North Sea. The cotidal lines show the progress of the tide each constituent hour (30 ' phase change), the dotted corange lines show the decrease in feet of the Mj tidal range away from the shore. From Doodson and Warburg ( 1941)- Equation 1 states that the time rate of change of the downchannel horizon
. Collected reprints / Atlantic Oceanographic and Meteorological Laboratories [and] Pacific Oceanographic Laboratories. Oceanography EQUATIONS OF MOTION 57 60° - 58° 56° - 54° - 52° - 50°. FIGURE 4. Amphidromic systems of the Mj tidal constituent (semidaily lunar tide) in the North Sea. The cotidal lines show the progress of the tide each constituent hour (30 ' phase change), the dotted corange lines show the decrease in feet of the Mj tidal range away from the shore. From Doodson and Warburg ( 1941)- Equation 1 states that the time rate of change of the downchannel horizontal velocity u is equal to the acceleration of gravity g multiplied by the downchannel slope of the sea surface, whose displacement above mean water is r\\ t is the time elapsed after high water at the source; and x is the distance away from the source of the tide as measured along the axis of the channel. Equation 2 states that the time rate of change of the sea surface displacement rj is equal to the mean depth h multiplied by the horizontal rate of change of the downchannel velocity u. Assuming that the mean depth h is uniform through- out the channel, a tide with a period T and an amplitude a (one-half the range) would be described by t? = a cos H-t)] â GT-GK'-f)] (3) (4) where c = (gh)112 is the speed of propagation at which the shape of the sea surface moves down the channel. For oceanic and shelf depths c is 200 and 31 m/sec, respectively. If the depth h were representative of the open ocean (h = 4000 m) and the amplitude of the tide were a = m, the maximum tidal current according to (4) would be cm/sec, a relatively small speed. On the other hand, if the depth were representative of the continental shelves (h = 100 m), the corresponding current would be cm/sec. For a given tidal ampli- tude, the maximum tidal currents are inversely pro- portional to the square root of depth. In very shallow water, where (4) would predict unrealistically large c
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