NUTATIONS INDUCED BY THE NON-TIDAL VARIATIONS
IN 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. de Viron, Goosse, Bizouard and Lambert have derived such an OAM series spanning 1997.0-2002.0, and computed the associated perturbation on nutation (practically the celestial pole offsets dX and dY) (communication done at EGS General Assembly 2002). We derived a model including 4 periodic circular components under the form :

dX + i dY = Sj (ainj + i aopj) ei cj
or :
dX = Sj ainj cos cj - aopj sin cj
dY = Sj aopj cos cj + ainj sin cj

where cj is integer linear combination of Delaunay arguments, GMST + p :
xi = a1 l + a2 l' + a3 D + a4 F + a5 W.

The model is reported in the table below together with the combined effect of the Atmospheric Angular Momentum (NCEP-NCAR reanalysis series). Two model of the oceanic behaviour in front of the atmospheric pressure variation are considered : Inverted Barometer (IB) and Non Inverted Barometer (NIB) (more realistic for the diurnal atmospheric/oceanic fluctuations which cause those perturbations on nutation). Incertainties are in parentheses. All these value have to be considered with caution, as a very approximate estimation of the non-tidal oceanic effect on nutation.

                  
l  l' F  D  W    PERIOD             ainj IB   aopj IB        ainj NIB   aopj NIB       
                (days)               (mas)      (mas)         (mas)      (mas)    
---------------------------------------------------------------------------------               
0  0  2 -2  2    182.2      OAM        5(5)     -1(5)          2(8)      -8(8)
                            AAM      -42(1)     11(1)        -45(3)      -2(3)  
                            total    -37(6)     10(6)        -43(11)    -10(11)
---------------------------------------------------------------------------------  
0  1  0  0  0    365.26     OAM      -44(9)     50(9)        -60(13)     80(13)
                            AAM      -71(2)     28(2)       -100(5)       3(5)
                            total   -115(11)    78(11)      -160(18)     83(18)
---------------------------------------------------------------------------------  
0 -1  0  0  0               OAM    87(144)    58(144)       133(205)   222(205)
                 -365.26    AAM     55(25)    -19(25)        -20(88)   -114(88)
                            total  142(169)    38(169)       113(293)   108(293)
      	   
								
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 -W  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 :
   W = 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.          

Rotation angle in arcseconds : Greenwich Mean Sidereal Time + 180°

   GMST + p = (67310.54841d0 + (876600d0*3600 + 8640184.812866d0) t 
             + 0.093104d0*t2 - 6.2 10-6 * t3 )*15.0d0 + 648000.0


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