Abstract
Eliassen and Palm (1961) has pointed out that two dimensional steady internal gravity waves do not accelerate the zonal mean flow if there is no external forces or dissipation, and Andrews and McIntyre (1978 a, b) have generalized this theorem. It is pointed out that the so-called “Eliassen-Palm relation” is the direct result from the conservations of energy and momentum of material layers by using the fact that energy and momentum fluxes through a material surface are connected by the phase velocity. From Lagrangian view point, it is shown that the difference between the Reynolds stress and the radiation stress results from the Lagrangian transversal flow due to the waves, and the“Eliassen-Palm relation” means in general that steady waves do not accelerate the mean flow in Lagrangian meaning.
In cases of three-dimensional rotational flow and quasi-geostrophic flow, this fact explains the meaning of Uryu's results (1973) and Charney and Drazin's results (1961), respectively. We can also obtain the mean flow acceleration when there are external forces and dissipation from the Lagrangian view point.
The theorem proved by Eliassen and Palm (1960) and generalized by Andrews and McIntyre (1976a) and also by Boyd (1976), is discussed from a somewhat different viewpoint from that so far.
