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Laplace transform integration of the shallow‐water equations. Part II: Semi‐Lagrangian formulation and orographic resonance
Author(s) -
Clancy Colm,
Lynch Peter
Publication year - 2011
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.805
Subject(s) - advection , orographic lift , laplace transform , scheme (mathematics) , lagrangian , waves and shallow water , resonance (particle physics) , eulerian path , mathematics , shallow water equations , mathematical analysis , meteorology , physics , precipitation , particle physics , thermodynamics
In this article we combine the Laplace transform (LT) scheme with a semi‐Lagrangian advection scheme, and implement it in a shallow‐water model. It is compared to a reference model using the semi‐implicit (SI) scheme, with both Eulerian and Lagrangian advection. We show that the LT scheme is accurate and computationally competitive with these reference schemes. We also show, both analytically and numerically, that the LT scheme is free from the problem of orographic resonance that is found with semi‐implicit schemes. Copyright © 2011 Royal Meteorological Society