A Divergence-Form Wave-Induced Pressure Inherent in the Extension of the Eliassen–Palm Theory to a Three-Dimensional Framework for All Waves at All Latitudes

Aiki, Hidenori, Takaya, Koutarou and Greatbatch, Richard John (2015) A Divergence-Form Wave-Induced Pressure Inherent in the Extension of the Eliassen–Palm Theory to a Three-Dimensional Framework for All Waves at All Latitudes Journal of the Atmospheric Sciences, 72 (7). pp. 2822-2849. DOI 10.1175/JAS-D-14-0172.1.

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Abstract

Classical theory concerning theEliassen–Palmrelation is extended in this study to allowfor a unified treatment
of midlatitude inertia–gravity waves (MIGWs), midlatitude Rossby waves (MRWs), and equatorial waves
(EQWs). A conservation equation for what the authors call the impulse-bolus (IB) pseudomomentum is useful,
because it is applicable to ageostrophic waves, and the associated three-dimensional flux is parallel to the direction
of the group velocity of MRWs. The equation has previously been derived in an isentropic coordinate system or
a shallow-water model. The authors make an explicit comparison of prognostic equations for the IB pseudomomentum
vector and the classical energy-based (CE) pseudomomentum vector, assuming inviscid linear waves
in a sufficiently weak mean flow, to provide a basis for the former quantity to be used in an Eulerian time-mean
(EM) framework. The authors investigate what makes the three-dimensional fluxes in the IB and CE pseudomomentum
equations look in different directions. It is found that the two fluxes are linked by a gauge transformation,
previously unmentioned, associated with a divergence-form wave-induced pressure L. The quantity L
vanishes for MIGWs and becomes nonzero for MRWs and EQWs, and it may be estimated using the virial
theorem. Concerning the effect of waves on the mean flow, L represents an additional effect in the pressure
gradient term of both (the three-dimensional versions of) the transformed EM momentum equations and the
merged form of the EMmomentumequations, the latter of which is associated with the nonacceleration theorem.

Document Type: Article
Keywords: Ageostrophic circulations, Lagrangian circulation/transport, Momentum, Potential vorticity, Rossby waves, Wave properties
Research affiliation: OceanRep > GEOMAR > FB1 Ocean Circulation and Climate Dynamics > FB1-TM Theory and Modeling
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
DOI etc.: 10.1175/JAS-D-14-0172.1
ISSN: 0022-4928
Related URLs:
Date Deposited: 09 Jul 2015 10:00
Last Modified: 09 Jul 2015 10:00
URI: http://eprints.uni-kiel.de/id/eprint/29210

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