| Linear computational stability analysis for a modified semi-implicit integration technique for gravity oscillations in a two layer model in Phillips [sigma] coordinate - :12327 | National Weather Service (NWS)
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Linear computational stability analysis for a modified semi-implicit integration technique for gravity oscillations in a two layer model in Phillips [sigma] coordinate
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    "In NMC Office Note 45, we presented an analysis of the linear computational stability of an explicit and an implicit formulation of the linear gravitational modes admitted by a two-layer model atmosphere expressed in Phillips' [sigma]-coordinate. The implicit method was unconditionally stable, whereas the explicit method displayed only conditional stability. There were two critical phase speeds involved in the explicit method's conditional stability criterion. For an isothermal basic state, the larger phase speed was close to that of the "Lamb wave." The second, slower mode, was referred to as the "internal mode." The phase speed of the internal mode is commensurate with the speed of advective winds found in the atmosphere, whereas the "Lamb wave" phase speed is a good deal larger"--Introduction.

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