The horizontal-vertical and isopycnal mixing of the previous two sections employed symmetric positive semi-definite tensors representing dissipative mixing processes. The presence of an anti-symmetric component to the mixing tensor, as seen in Section B.1, can be thought of as an added advective transport of tracers [see in particular the equations leading up to (B.19)]. The transport velocity defined by such a tensor is divergence-free [equation (B.16)] and preserves all tracer moments if it has zero normal value on the boundaries [discussion following equation (B.34)]. The parameterization of Gent and McWilliams (1990) has been reformulated in terms of such an effective transport velocity by Gent et. al., (1995). Other types of mixing can be parameterized by anti-symmetric mixing tensors. For example, Middleton and Loder (1989) summarize the effects of mixing by non-zero angular momentum waves which gives rise to skew-fluxes.