with distance and cause the ocean's surface to deviate from the geoid. They establish a new equilibrium ocean surface which bulges toward the moon on one side and away from the moon on the other side. The earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface tends toward this equilibrium shape, which is constantly changing, and never quite attains it. When the ocean surface is not aligned with it, it's as though the surface is sloping, and water accelerates in the down-slope direction. Equilibrium The equilibrium tide is the idealized tide assuming a landless Earth. It would produce a tidal bulge in the ocean, elongated towards the attracting body (Moon or Sun). It is not caused by the vertical pull nearest or farthest from the body, which is very weak; rather, it is caused by the tangent or "tractive" tidal force, which is strongest at about 45 degrees from the body, resulting in a horizontal tidal current. Laplace's tidal equations Ocean depths are much smaller than their horizontal extent. Thus, the response to tidal forcing can be modelled using the Laplace tidal equations which incorporate the following features: The vertical (or radial) velocity is negligible, and there is no vertical shear—this is a sheet flow. The forcing is only horizontal (tangential). The Coriolis effect appears as an inertial force (fictitious) acting laterally to the direction of flow and proportional to velocity. The surface height's rate of change is proportional to the negative divergence of velocity multiplied by the depth. As the horizontal velocity stretches or compresses the ocean as a sheet, the volume thins or thickens, respectively. The boundary conditions dictate no flow across the coastline and free slip at the bottom. The Coriolis effect (inertial force) steers flows moving towards the Equator to the west and flows moving away from the Equator toward the east, allowing coastally trapped waves. Finally, a dissipation term can be added which is an analog to viscosity. Amplitude and cycle time The theoretical amplitude of oceanic tides caused by the Moon is about at the highest point, which corresponds to the amplitude that would be reached if the ocean possessed a uniform depth, there were no landmasses, and the Earth were rotating in step with the Moon's orbit. The Sun similarly causes tides, of which the theoretical amplitude is about (46% of that of the Moon) with a cycle