Laplace transform integration of the shallow‐water equations. Part I: Eulerian formulation and Kelvin waves

A filtering integration scheme is developed, using a modification of the contour used to invert the Laplace transform (LT). It is shown to eliminate components with frequencies higher than a specified cut‐off value. Thus it is valuable for integrations of the equations governing atmospheric flow. The scheme is implemented in a shallow‐water model with an Eulerian treatment of advection. It is compared to a reference model using the semi‐implicit (SI) scheme. The LT scheme is shown to treat dynamically important Kelvin waves more accurately than the SI scheme. Copyright © 2011 Royal Meteorological Society