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Four‐dimensional tensor equations for a classical fluid in an external gravitational field
Author(s) -
Charron Martin,
Zadra Ayrton,
Girard Claude
Publication year - 2014
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.2185
Subject(s) - christoffel symbols , formalism (music) , covariant transformation , gravitational field , classical mechanics , metric tensor , field equation , gravitation , physics , conservation law , equations of motion , lanczos tensor , mathematical physics , einstein tensor , tensor density , tensor field , exact solutions in general relativity , mathematics , riemann curvature tensor , mathematical analysis , geometry , curvature , art , musical , visual arts , geodesic
A four‐dimensional tensor formalism suitable for the equations of motion of a classical fluid in the presence of a given external gravitational field is presented. The formalism allows for arbitrary time‐dependent transformations of spatial coordinates. Some well‐known conservation laws are derived in covariant form. The metric tensor and the associated Christoffel symbols are calculated for coordinate systems useful in meteorology. The vertical momentum equation employed in the Canadian operational weather forecasting model is obtained using the proposed tensor formalism.