Tides in Ocean Basins Background

In other sections, our discussion of tides has assumed a water-covered Earth that rotates on its spin axis through the tidal bulges. In a more realistic situation, many non-astronomical factors modify ocean tides, including the presence of continents, the Coriolis effect, winds, and variations in coastline configuration, water depth, and bottom topography. Tidal bulges move relatively unimpeded around the globe only in the Southern Ocean near Antarctica. Consider, for example, the idealized case of tides in a Northern Hemisphere ocean basin of uniform depth that is completely surrounded by land. Assume also that the moon is providing the only tide-generating force and initially is situated directly above the ocean basin.
 
As Earth rotates from west to east, the tidal bulge shifts toward the western boundary of the ocean basin and the water surface slopes gently downward toward the east. The western boundary of the basin experiences high tide while the eastern boundary experiences low tide. Tide waves are shallow-water waves. Hence, as noted earlier in this chapter, the orbits of water particles flatten with increasing depth, changing from circular to elliptical and ul­timately to a back-and-forth motion near the ocean bottom. The horizontal motion of water particles in a tide persists for long periods (because the tide wave is con­stantly being forced) so that the tide wave is subject to the Coriolis effect. As the tidal bulge at the western boundary begins to move down slope toward the east, the Coriolis deflects water particles to the right (in the Northern Hemi­sphere) so that the tidal crest (high tide) rotates into the southern portion of the basin. Now, the water surface slopes downward toward the north. The tidal crest continues to rotate around the basin in a counterclockwise direction (viewed from above). When the tide is high on one side of the basin, it is low on the opposite side. In Southern Hemi­sphere basins, the reversal of the Coriolis deflection causes the tide wave to rotate in a clockwise direction (viewed from above).
 
This so-called dynamic model of tides applies rea­sonably well to seas and large embayments as well as the open ocean. Ocean scientists graphically represent the ro­tary motion of the tide wave in a basin by a series of cotidal lines radiating outward from a central node like the spokes in a bicycle wheel. A cotidal line joins points where high tide occurs at the same time of day; they are usually drawn at one-hour intervals. The tidal range varies from zero at the node to a maximum at the antinode along the coast.
 
Diurnal tides make one complete circuit per tidal day whereas semidiumal or mixed tides complete two cir­cuits per tidal day. The period of the rotary tide waves is 12 hrs 25 min for semidiurnal tides and 24 hrs 50 min for diurnal tides. For an ocean of average depth (about 4000 to or 13,000 ft), a tide wave progresses as a shallow-water wave at about 645 km (400 mi) per hr. (As with wind generated water waves, this is the speed of the wave energy, not the water.) Actual wave celerity along the coast varies greatly due to topography. Along the west coast of the U.S., lode waves travel at about 565 km (350 mi) per hr, whereas along the west coast of Africa in the Northern Hemisphere, speeds are about 360 km (225 mi) per hr. For coastal residents, however, these high speeds are not apparent because for a diurnal tide, a 2-m (6.5-ft) rise in water may take slightly more than 6 hrs.