Sb. Vosper et Sd. Mobbs, Momentum fluxes due to three-dimensional gravity-waves: Implications for measurements and numerical modelling, Q J R METEO, 124(552), 1998, pp. 2755-2769
Citations number
17
Categorie Soggetti
Earth Sciences
Journal title
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY
A three-dimensional wave-action equation for linear internal gravity-waves
is derived. When the basic-state flow does not turn with height, this equat
ion can be used to derive the three-dimensional version of a theorem of Eli
assen and Palm. This states that, for steady flows in the absence of dissip
ation, the vertical flux of both horizontal components of momentum is indep
endent of height. When the basic-state flow exhibits turning with height, a
nalysis of the wave-action equation indicates that, in general, the wave fi
eld cannot be regarded as steady and the three-dimensional Eliassen and Pal
m theorem does not apply. It is also shown that the wave-action equation ha
s serious implications for the interpretation of atmospheric measurements o
f the momentum flux: in order to make accurate measurements of the momentum
flux arising from three-dimensional orographically forced gravity-waves, i
t is necessary to average rho(m)u'w' (where rho(m) is the basic-state densi
ty and u' and w' are the horizontal and vertical wave-induced velocity-pert
urbations respectively) on horizontal planes downstream of the orography, r
ather than along lines in the downstream direction (as has previously been
done with aircraft measurements). Using a three-dimensional linear numerica
l model, we demonstrate the importance of this in even the most simple idea
lized cases.