We wish to thank Geoff Vallis and an anonymous reviewer for exceptionally constructive and thorough reviews that led to a much improved manuscript. We also thank Bill Young and Xiaoming Zhai for additional insightful comments. Financial support was provided by the UK Natural Environment Research Council (NE/H020454/1).
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One may also consider this constraint as a conservation of angular momentum; conservation of zonal momentum in the rotating frame is equivalent to conservation of angular momentum in an inertial frame.
Young has pointed out that E should be defined as two separate vectors, because E does not, in general, transform as a tensor (W. R. Young 2011, personal communication). However, in the quasigeostrophic limit we consider for the remainder of this paper, E does transform as a tensor under horizontal transformations and might therefore be termed a “quasigeostrophic tensor.”
Note that the signs of the fluxes M and N are defined inconsistently in the literature.
Weighting of vertical components by factors of