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Semi‐geostrophic solutions for flow over a ridge
Author(s) -
Cullen M. J. P.
Publication year - 2007
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.15
Subject(s) - geostrophic wind , limit (mathematics) , rossby number , ridge , mathematics , terrain , orography , convergence (economics) , boundary (topology) , flow (mathematics) , mathematical analysis , geology , geodesy , meteorology , geometry , physics , geography , climatology , precipitation , paleontology , cartography , economic growth , turbulence , economics
An algorithm for solving the semi‐geostrophic (SG) equations using real physical variables in terrain‐following coordinates is developed and used to demonstrate the expected rate of convergence of solutions of the complete equations of motion to SG solutions as the Rossby number is reduced. The tests are carried out with significant orography in a vertical slice geometry. Two asymptotic limits are tested. The SG limit is singular in one of the limits and smooth in the other. The results show the validity of using the SG model for diagnostic purposes in appropriate regimes. They also expose a number of boundary condition and numerical issues, showing that comparison with rigorous error estimates is a useful way of validating numerical procedures. © Crown Copyright 2007. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd