  Expressions for local discrete variance decay (DVD) rates are directly
derived from discrete tracer equations without any assumptions on discrete
fluxes of the second moment. Spurious mixing (SM) associated with numerical
implementations of scalar advection and diffusion is thus estimated. The new
framework is shown to avoid the need for second-moment flux definition when
solved on finite-volume cell edges but still invoke certain second-moment
fluxes when the DVD rates are partitioned to participating cell nodes. These
implied discrete fluxes are shown to differ from those proposed in earlier
literature (but share the same dissipative part) and thus reveal the
non-uniqueness of their nature. They are shown to be ambiguous for high-order
advection schemes introducing uncertainty to the locality of any estimates
produced by a DVD approach. Additional damping of flux divergence through
temporal averaging or some coarse-graining is thus shown to be necessary.
Through the application of this technique, SM is found to be correlated with
the distribution of eddy kinetic energy. The contribution from vertical
advection to SM is found to be relatively small and correlated with the
distribution of buoyancy fluxes. The explored high-order schemes are found to
demonstrate levels of spurious mixing which may locally exceed background
physical mixing.
