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High and low tide in the Bay of Fundy. The theory of tides is the application of continuum mechanics to interpret and predict the tidal deformations of planetary and satellite bodies and their atmospheres and oceans (especially Earth's oceans) under the gravitational loading of another astronomical body or bodies (especially the Moon and Sun).
The oscillation periods of the Earth as a whole are not near the astronomical periods, so its flexing is due to the forces of the moment. The tide components with a period near twelve hours have a lunar amplitude (Earth bulge/depression distances) that are a little more than twice the height of the solar amplitudes, as tabulated below.
The largest annual tidal range can be expected around the time of the equinox if it coincides with a spring tide. Spring tides occur at the second and fourth (last) quarters of the lunar phases . By contrast, during neap tides , when the Moon and Sun's gravitational force vectors act in quadrature (making a right angle to the Earth's orbit ...
More precisely, the lunar tidal acceleration (along the Moon–Earth axis, at the Earth's surface) is about 1.1 × 10 −7 g, while the solar tidal acceleration (along the Sun–Earth axis, at the Earth's surface) is about 0.52 × 10 −7 g, where g is the gravitational acceleration at the Earth's surface.
A Kelvin wave is a special type of gravity wave that can exist when there is (1) gravity and stable stratification, (2) sufficient Coriolis force and (3) the presence of a vertical boundary. [12] Kelvin waves are important in the ocean and shelf seas, they form a balance between inertia, the Coriolis force and the pressure gradient force.
The Hawaiian Ridge produces depth-integrated energy fluxes as large as 10 kW/m. The longest wavelength waves are the fastest and thus carry most of the energy flux. Near Hawaii, the typical wavelength of the longest internal tide is about 150 km while the next longest is about 75 km. These waves are called mode 1 and mode 2, respectively.
For example, the lunar tidal acceleration at the Earth's surface along the Moon–Earth axis is about 1.1 × 10 −7 g, while the solar tidal acceleration at the Earth's surface along the Sun–Earth axis is about 0.52 × 10 −7 g, where g is the gravitational acceleration at the Earth's surface.
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.