Decomposition of Global Ocean Currents Using a Simple Iterative Method

Abstract

The common representation of two-dimensional nondivergent oceanic currents or fluxes by a streamfunction is extended to the divergent global case using the Helmholtz decomposition of the flow into rotational (nondivergent) and divergent (irrotational) components, represented by stream- and potential functions, respectively. An appropriate discretization of the problem, in either horizontal or vertical planes, is described. While a standard numerical solver of the Poisson equation for the streamfunction in the spherical, horizontal problem does not constrain the rotational flow to the ocean, a simple iterative procedure is used to do this. This involves modifying the coastal vorticity at each step by resetting the flow over land to zero. The scheme is easily programmed and efficiently determines the streamfunction for realistic flows. The potential can then be determined simply. The decomposition of the time-mean volume fluxes simulated by the Commonwealth Scientific and Industrial Research Organisation ocean general circulation model is considered to illustrate the approach. For the horizontal case, the decomposition of fluxes within the model layers is presented. The gyres within each ocean basin are represented by a streamfunction for each layer, while the potential function represents overturning flows. As an example of the latitude-depth case, the decomposition of the simulated Atlantic sector circulation extends the usual streamfunction into the Southern Ocean. The decomposition of flow in the equatorial longitude-depth plane represents both the westward surface flux and the eastward undercurrent via a streamfunction. A brief comparison of the decomposition with other approaches is made.