NUTATIONS INDUCED BY THE NON-TIDAL OCEANIC ANGULAR MOMENTUM

Non-tidal fluctuations in water heigh and currents at diurnal periods (partly caused by atmospheric wind and pressure variations) induce retrograde diurnal variations of the equatorial oceanic angular momentum (OAM), hence nutations. They can be estimated from angular momentum time series associated with various Ocean Global Circulation Models.

One can found estimates in Brzezinski et al. (2004), Tab. 1 under the form

dX + i dY = Σj(ainj + i aopj) ei χj
or
dX = Σjainj cos χj - aopj sin χj
dY = Σjaopj cos χj + ainj sin χj

where
• χj is integer linear combination of Delaunay arguments: χi = a1 l + a2 l' + a3 D + a4 F + a5 Ω .
• ainj represents the in-phase term (w.r.t. luni-solar rigid Earth nutation), aoutj the out-of-phase term
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Delaunay arguments
(IERS Conventions 2000, from Simon et al., 1994, Astron. Astrophys. 282, 663-683):

Mean anomaly of the Moon :
l = 134°.963 402 51 + 1 717 915 923.2178" t + 31".879 2 t2 + 0".051 635 t3 - 0".000 244 70 t4

Mean anomaly of the Sun  :
l'= 357°.529 109 18 +   129 596 581.0481" t - 0".553 2 t2 -  0".000 136 t3 - 0".000 011 49 t4

F = L -Ω  with L mean longitude of the Moon
F =  93°.272 090 62 + 1 739 527 262.8478" t - 12".751 2 t2 - 0".001 037 t3 + 0".000 004 17 t4

Mean elongation of the Moon from the Sun :
D = 297°.850 195 47 + 1 602 961 601.2090" t -  6".370 6 t2 + 0".006 593 t3 - 0".000 031 69 t4

Mean longitude of the ascending node of the Moon :
Ω = 125°.044 555 01  - 6 962 890.543 1" t + 7".472 2 t2 + 0".007 702 t3 - 0".000 059 39 t4

where t is measured un Julian Centuries of 36525 days of 86400 seconds of Dynamical Time since J2000.0.
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