The Computation of Diapycnal Diffusive and Advective Scalar Fluxes in Multilayer Isopycnic-Coordinate Ocean Models

Abstract

This paper addresses the problem of how to numerically incorporate diapycnal mixing and advection processes into isopycnal ocean general circulation models. A general expression of diapycnal velocity is derived for the case in which density is a function of both potential temperature and salinity. The expression is independent of turbulence closure parameterizations and thus can be viewed as a generalized definition of diapycnal velocity. With this definition, it is simple to derive expressions of diapycnal velocity for different parameterizations of turbulent mixing in isopycnal ocean models. Numerical algorithms are developed to overcome difficulties associated with massless layers in computing diapycnal diffusive and advective scalar fluxes in isopycnic-coordinate ocean models. In the diapycnal diffusive flux computation, a mass-weighted averaging is used to prevent linear instability in the time integration. In diapycnal advective flux computation, it is shown that the diapycnal mass exchange associated with density coordinate restoration should be consistent with that caused by diapycnal velocity. This consistency is achieved in the developed algorithms. The algorithms are tested and verified in one-dimensional Dirichlet and Neumann boundary value problems. Furthermore, through a simulation of a realistic ocean profile diffusion process, the author shows that the algorithms not only have the ability to simulate vertical mixing processes in the real ocean but also have computational efficiency good enough for application to three-dimensional isopycnal ocean models.