The traditional manner of parameterizing tracer mixing in ocean models is through the use of a second order mixing tensor. The basic mathematical properties of such mixing have been reviewed in this appendix. In general, the mixing tensor contains both a symmetric positive-semi-definite component and an anti-symmetric component. The symmetric component represents dissipative processes associated with diffusive mixing. The numerical discretization of this process is discussed further in Appendix C. The anti-symmetric component can be formulated in terms of an advective velocity which, in addition to the usual Eulerian velocity, contributes to conservative tracer mixing.
Because there will always be mixing processes too small to resolve in
ocean models, there will always be a need to rationally parameterize
these processes. Determining the nature of mixing tensors relevant
for these parameterizations, if such objects exist, is proving to be
one of the most challenging problems in physical oceanography today.