The Eliassen–Palm flux tensor

The aim of this paper it to derive general coordinate-invariant forms of the Eliassen–Palm flux tensor and thereby characterize the true geometric nature of the eddy–mean-flow interaction in hydrostatic Boussinesq rotating fluids. In the quasi-geostrophic limit previous forms of the Eliassen–Palm fl...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2013-08, Vol.729, p.69-102
Main Authors: Maddison, J. R., Marshall, D. P.
Format: Article
Language:English
Subjects:
Boussinesq equations
Buoyancy
Earth, ocean, space
Exact sciences and technology
External geophysics
Fluctuations
Fluid dynamics
Flux
Hydrostatics
Mathematical analysis
Navier-Stokes equations
Oceans
Physics of the oceans
Tensors
Thermodynamics
Thermohaline structure and circulation. Turbulence and diffusion
Transformations
Turbulence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The aim of this paper it to derive general coordinate-invariant forms of the Eliassen–Palm flux tensor and thereby characterize the true geometric nature of the eddy–mean-flow interaction in hydrostatic Boussinesq rotating fluids. In the quasi-geostrophic limit previous forms of the Eliassen–Palm flux tensor are shown to be related to each other via a gauge transformation; a general form is stated and its geometric properties are discussed. Similar methodology is applied to the hydrostatic Boussinesq Navier–Stokes equations to re-derive the residual-mean equations in a coordinate-invariant form. Thickness-weighted averaging in buoyancy coordinates is carefully described, via the definition of a volume-form-weighted average, constructed so as to commute with the covariant divergence of a vector. The procedures leading to the thickness-weight averaged equation are discussed, and forms of the Eliassen–Palm flux tensor which arise are identified.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2013.259