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The Energetically Consistent Shallow-Water Equations

Peter R. Gent

Open publisher page 54 citations

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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What this paper is about

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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Available 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.

Key concepts: Isopycnal, Diabatic, Shallow water equations, Primitive equations, Waves and shallow water, Oscillation (cell signaling), Dynamical systems theory, Physics

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