Effect of topographic barriers on the rates of available potential energy conversion of the oceans

Determining the energy budget of the oceans requires evaluating the rates of available potential energy conversion in the circulation. Calculating these conversion rates depends upon the definition of an appropriate "reference" state of the density field, but this definition is complicated in the oceans by the presence of bottom topography. The trapping of dense fluid by topographic barriers means that there are multiple definitions for the reference state. The approach taken in this paper is to examine the sensitivity of the available potential energy budget to several methods for defining the reference state. The first method makes allowances for restrictions imposed on the flow by topography, however it is computationally intensive. The second method is proposed as an inexpensive alternative to the first. These new methods are used to evaluate the energy budget of a model overturning circulation maintained by surface buoyancy forcing. The results are compared with those obtained from two existing methods; one which employs an adiabatic resorting procedure ignoring topography, and one which uses a reference profile developed from the horizontal average of the density field. In our model, the rates of available potential energy conversion are insensitive to the reference state definition providing the reference state is developed from an adiabatic resorting of the domain. These results suggest that any of the adiabatic resorting methods proposed here would be sufficient to evaluate the rates of energy conversion in the ocean