On thermobaric production of potential vorticity in the ocean

Abstract

Because of the two-constituent nature of seawater, there is no conservative potential vorticityfor the ocean, even when viscous and diffusive effects are ignored. Specifically, nonconservationarises in association with the thermobaric effect, which is related to nonlinearities in the equationof state. While this is well-known, it is generally supposed that this forcing is far too small tobe of importance for most problems of interest. A careful scale analysis is presented to suggestthat thermobaric forcing is larger than is generally supposed, particularly at the high wavenumberend of the spectrum. The spatial structure of the thermobaric potential vorticity sourceis dependent on an arbitrary choice, such as the choice of a reference pressure in the definitionof potential vorticity. To address the effect of thermobaricity on the dynamics, which must beindependent of arbitrarily chosen parameters, it therefore seems desirable to consider howbalanced dynamical systems are affected. In this spirit, an analog to quasigeostrophy that isapplicable to thermobaric fluids is derived and its conservation properties are discussed. It isargued that thermobaricity can lead to O(1) changes in the vorticity distribution at the highwavenumber end of the spectrum. Additionally, integral constraints that can influence basinscale circulation are affected. For example, isopycnal mixing affects the (QG) energetics andpotential enstrophy is lost as a conserved quantity. The size of the enstrophy source (or sink)and the wave number at which thermobaric effects produce an O(1) effect both depend on thesize of a nondimensional parameter that is introduced. This parameter, although typically small,can be large with respect to the Rossby number appropriate to the mid-latitude eddy field.That is, it is suggested that thermobaric effects may be larger than finite Rossby number effectson the dynamics of the mid-latitude eddy field, particularly below the thermocline.