Energetics of Geostrophic Adjustment in Rotating Flow

Abstract: Energetics of geostrophic adjustment in rotating flow is examined in detail with a linear shallow watermodel. The initial unbalanced flow considered first falls under two classes. The first is similar to thatadopted by Gill and is here referred to as a mass imbalance model, for the flow is initially motionless butwith a sea surface displacement. The other is the same as that considered by Rossby and is referred to as amomentum imbalance model since there is only a velocity perturbation in the initial field. The significantfeature of the energetics of geostrophic adjustment for the above two extreme models is that although theenergy conversion ratio has a large case-to-case variability for different initial conditions, its value isbounded below by 0 and above by 1/2. Based on the discussion of the above extreme models, the energeticsofadjustment for an arbitnary initial condition is investigated. It is found that the characteristics of the ener-getics of geostrophic adjustment mentioned above are also applicable to adjustment of the general unbal-anced flow under the condition that the energy conversion ratio is redefined as the conversion ratio betweenthe change of kinetic energy and potential energy of the deviational fields.

Keywords:
• geostrophic adjustment,
• energy conversion ratio,
• mass imbalance,
• momentum imbalance,
• kine- tic energy,
• potential energy