Mathematics
Scientific paper
Jul 1974
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974jats...31.1421l&link_type=abstract
Journal of Atmospheric Sciences, vol. 31, Issue 5, pp.1421-1446
Mathematics
32
Scientific paper
A numerical program is developed to study the behavior of atmospheric tides in atmospheres with arbitrary distributions (with respect to altitude and latitude) of mean temperature and zonal wind. This program is used to calculate solar and lunar semidiurnal tides for various realistic models of seasonal distributions of wind and temperature.We find that the main effect of winds on the solar semidiurnal tide (for which we have thermal excitation distributed from the ground to about 80 km) is to give rise to significant mode coupling between the main semidiurnal mode and higher modes-leading to an enhancement of the latter. The main consequences of this coupling are to (i) shift the height at which a 180° phase shift for pressure and wind fields is predicted from about 28 km (the value without winds) to substantially greater heights during the summer at middle and high latitudes; (ii) cause higher order modes to dominate semidiurnal wind oscillations near 100 km at middle and high latitudes; and (iii) reduce the amplitude at 100 km of the main semidiurnal mode by about 40% compared with what one would obtain in the absence of mean winds. All the above are shown to be consistent with recent observations.For the lunar semidiurnal tide, the present calculations also offer new insight. If one ignores mean winds then gravitational forcing appears mathematically as a coherent drive at the earth's surface. For such forcing, previous calculations have demonstrated an immense sensitivity of tidal magnitudes to the details of the assumed vertical distribution of mean temperature. This sensitivity arose because multiple reflections due to thermal inhomogeneities could (since in the absence of horizontal temperature gradients, surfaces of constant `index of refraction' are horizontal) lead to strong constructive or destructive interference depending on small variations in temperature. The inclusion of realistic damping mitigated the sensitivity somewhat, but the sensitivity remained much greater than what one would infer from data. When one includes mean winds and horizontal temperature gradients, surfaces of constant index of refraction get `bent' and the possibilities of consistent interference diminish drastically. Indeed, our calculations show very little sensitivity to details of assumed temperature. In all cases amplitudes close to those observed are predicted
Hong Siu-Shung
Lindzen Richard S.
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