Dynamic Theory of Tides

Tidal lag:

• At the equator, the surface of the earth is moving at ~ 460 m/s

• The tide is a shallow-water wave, so it travels at a speed C = sqrt ( g * depth)

• For the tide wave to keep up with the Earth, the ocean would have to be 22,000 m deep!

• Average depth is ~ 4000 m, so between 26 degrees N/S, the lag is 90 degrees (indirect tide) and beyond 65 degrees N/S, the tide lag disappears (direct tide)

Coriolis Force:

• Lateral water movements are subject to the Coriolis force

• Laplace's Tidal Equations allow us to calculate the motion

local acceleration + Coriolis acceleration = pressure gradient force + astronomical force

• tides travel as rotary waves in ocean basins

Continents, Bathymetry and Friction

• The speed at which the tide wave can propagate depends on water depth

• The shape of ocean basins (e.g. open, closed, wide, narrow) determines the behavior of the tide wave

• Friction acts to slow the tide wave, and an equal, opposite friction force is exerted on the solid Earth, slowing its rotation

Large-scale rotary motion of tides in ocean basins creates an amphidromic system.

Global map of M 2 tide calculated from Topex/Poseidon observations of the height of the sea surface combined with the response method for extracting tidal information. Full lines are contours of constant tidal phase; gray scale gives the tidal amplitude (Center for Space Research, University of Texas).

Instead of circumnavigating the world, the tide wave is broken up into numerous smaller cells, called amphidromic systems. Within each cell, the tide wave circles around an amphidromic point.

Sources

Author: E. Boyce

Created: 7 December, 2003

Web project for PHYS645 Fundamentals of Geophysical Fluid Dynamics, University of Alaska Fairbanks