Long-period tides
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Long-Period tides are gravitational tides generated by the Earth's position relative to the Sun, Moon, and Jupiter. They are distinguished from the semi-diurnal and diurnal tides in having periods longer than one day and in the gravitational forcing being zonally symmetric. The amplitudes are generally less than 1 cm, so that they are treated as a kind of approximation to static equilibrium. Long-period tipdes are relatively weak, and their vorticity is zero, the periods and structures of the long period tides are known with very high precision, and no ambiguity deriving from their uncertainty propagates through the observations or theory.[1]
Formation mechanism
Tides are caused by relative location of the Earth, sun, and moon, whose motions are well known. The primary tidal frequency is semidiurnal diurnal that can be explained by the period of moon, which is one of tide-generating bodies, rotating around earth. So how to explain those longer periods? This is because the tide-generating bodies are not always in the same equatorial plane of earth, so the tide-generating forces vary with time, and this variation can be decomposed into different components ranging from semidiurnal to even thousands of years. The longer period forces generate long-period tides.
Oceanic response
Wunsch examined the tide gauge records from island in the tropical and sub-tropical Pacific then found the response to long-period tides are dominated by the generation at the lateral boundaries of barotropic Rossby wave.[2] Miller,[3] using a numerical model, found that in the Pacific Ocean at least, the dominant response was produced by a Kelvin wave response propagating from a generation region in the Arctic Ocean.
Effect on lunar orbit
The effect of long-period tides on lunar orbit is a controversial topic, some literatures conclude the long-period tides accelerate the moon and slow down the earth.[4][5] However Cheng [6] found that dissipation of the long-period tides brakes the moon and actually accelerates the earth's rotation. To explain this, they assumed the earth's rotation depends not directly on the derivation of the forcing potential for the long period tides, so the form and period of the long-period constituents is independent of the rotation rate. For these constituents, the moon (or sun) can be thought of as orbiting a non-rotating earth in a plane with the appropriate inclination to the equator. Then the tidal "bulge" lags behind the orbiting moon thus decelerating it in its orbit (bringing it closer to the earth), and by angular momentum conservation, the earth's rotation must accelerate. But this argument is qualitative, and a quantitative resolution of the conflicting conclusions is still needed.[1]
Pole tide
The ocean pole tide is caused by the variation of both the solid Earth and the oceans to the centrifugal potential that is generated by small perturbations to the Earth's rotation axis. The period of pole tides are 433 days (called the Chandler wobble) and annual. As this period is so long, the pole tide's displacement can be treated as in equilibrium with the forcing centrifugal potential. To model the pole tide, we need the so-called Love numbers and time series of perturbations to the Earth’s oration axis, which can be measured with satellite.[7]
Usage
The long-period tides are very useful for geophysicists, who use them to calculate the elastic Love number and to understand low frequency and large-scale oceanic motions.
References
- ^ a b Wunsch, Carl, Haidvogel D.B., Iskandarani M. (1997). "Dynamics of the long-period tides" (PDF). Progress in Oceanography. 40 (1): 81–108. doi:10.1016/S0079-6611(97)00024-4.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - ^ Wunsch C (1967). "The long-period tides". Rev. Geophys. 5 (4): 447–475. Bibcode:1967RvGSP...5..447W. doi:10.1029/RG005i004p00447.
- ^ Miller A.J., Luther D.S., Hendershott M.C. (1993). "The fortnightly and monthly tides: resonant Rossby waves or nearly equilibrium gravity waves?" (PDF). Journal of Physical Oceanography. 23 (23): 879–897. doi:10.1175/1520-0485(1993)023<0879:TFAMTR>2.0.CO;2.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - ^ Christodoulidis D.C., Smith D.E., Williamson R.G., Klosko S.M. (1988). "Observed tidal braking in the Earth/Moon/Sun system". Journal of Geophysical Research. 93 (B6): 6216–6236. Bibcode:1988JGR....93.6216C. doi:10.1029/JB093iB06p06216.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - ^ Marsh J.G., Lerch F.J., Putney B.H., Felsentreger T.L., Sanchez B.V., Klosko S.M., Patel G.B., Robbins, J.W., Williamson R.G., Engelis T.E. (1990). "The GEM‐T2 Gravitational Model". Journal of Geophysical Research: Solid Earth (1978–2012). 95 (B13): 22043–22071. Bibcode:1989gem..rept.....M. doi:10.1029/JB095iB13p22043.
{{cite journal}}: CS1 maint: multiple names: authors list (link) - ^ Cheng M.K., Lanes R.J., Tapley B.D. (1992). "Tidal deceleration of the Moon's mean motion". Geophysical Journal International. 108 (2): 401–409. Bibcode:1992GeoJI.108..401C. doi:10.1111/j.1365-246X.1992.tb04622.x.
{{cite journal}}: CS1 maint: multiple names: authors list (link) CS1 maint: unflagged free DOI (link) - ^ Desai S.D. (2002). "Observing the pole tide with satellite altimetry" (PDF). J. Geophys. Res. 107 (C11): 3186. doi:10.1029/2001JC001224.