Premium
A variational formulation of geophysical fluid motion in non‐Eulerian coordinates
Author(s) -
Dubos Thomas
Publication year - 2016
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.2942
Subject(s) - covariant transformation , curvilinear coordinates , eulerian path , equations of motion , generalized coordinates , classical mechanics , inertial frame of reference , variational principle , coordinate system , orthogonal coordinates , lagrangian and eulerian specification of the flow field , bipolar coordinates , action angle coordinates , physics , spherical coordinate system , calculus of variations , reference frame , mathematics , mathematical analysis , mathematical physics , geometry , frame (networking) , computer science , telecommunications , lagrangian
Systematic methods to derive geophysical equations of motion possessing conservation laws for energy, momentum and potential vorticity have recently been developed. One approach is based on Hamilton's least action principle in Eulerian curvilinear coordinates and the other is based on the covariance upon time‐dependent changes of spatial coordinates. The variational approach unifies, facilitates and generalizes the formulation of a wide range of approximations. The covariant approach makes it straightforward to rewrite approximate equations of motion derived in a particular coordinate system in another coordinate system. The variational approach encompasses models that, like the β ‐plane and non‐traditional shallow‐atmosphere approximations, lack a global inertial frame, so that the resulting motion cannot be interpreted as Newtonian motion observed in a non‐inertial frame. It has been previously suggested that such models are not covariant. In this work a covariant variational formulation is developed. As a consequence, it is shown that all models previously obtained by the variational approach are covariant upon time‐dependent changes of spatial coordinates.