| Abstract: This paper formulates tracer stirring arising from
the Gent-McWilliams (GM) eddy-induced transport in terms of a skew-diffusive
flux. A skew-diffusive tracer flux is directed normal to the tracer gradient,
which is in contrast to a diffusive tracer flux directed down the tracer
gradient. Analysis of the GM skew flux provides an understanding of the
physical mechanisms prescribed by GM stirring, which is complementary to
the more familiar advective flux perspective. Additionally, it unifies
the tracer mixing operators arising from Redi isoneutral diffusion and
GM stirring. This perspective allows for a computationally efficient and
simple manner in which to implement the GM closure in z-coordinate
models. With this approach, no more computation is necessary than when
using isoneutral diffusion alone. Additionally, the numerical realization
of the skew flux is significantly smoother than the advective flux. The
reason is that to compute the skew flux, no gradient of the diffusivity
or isoneutral slope is taken, whereas such a gradient is needed for computing
the advective flux. The skew-flux formulation also exposes a striking cancellation
of terms that results when the GM diffusion coefficient is identical to
the Redi isoneutral diffusion coefficient. For this case, the horizontal
components to the tracer flux are aligned down the horizontal tracer gradient,
and the resulting computational cost of Redi diffusion plus GM skew diffusion
is roughly half that needed for Redi diffusion alone. |