The Energetically Consistent Shallow-Water Equations

Peter R. Gent National Center for Atmospheric Research, Boulder, Colorado

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Abstract

It is shown that the very frequently used form of the viscous, diabatic shallow-water equations are energetically inconsistent compared to the primitive equations. An energetically consistent form of the shallow-water equations is then given and justified in terms of isopycnal coordinates. Examples are given of the energetically inconsistent shallow-water equations used in low-order dynamical systems and simplified coupled models of tropical air–sea interaction and the E1 Niño–Southern Oscillation phenomena.

Abstract

It is shown that the very frequently used form of the viscous, diabatic shallow-water equations are energetically inconsistent compared to the primitive equations. An energetically consistent form of the shallow-water equations is then given and justified in terms of isopycnal coordinates. Examples are given of the energetically inconsistent shallow-water equations used in low-order dynamical systems and simplified coupled models of tropical air–sea interaction and the E1 Niño–Southern Oscillation phenomena.

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