@article{fdi:010044261,
  title = {{S}purious diapycnal mixing in terrain-following coordinate models : the problem and a solution},
  author = {{M}archesiello, {P}atrick and {D}ebreu, {L}. and {C}ouvelard, {X}avier},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. {T}his error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. {I}n the case of {ROMS}, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. {W}e show that the common idea that spurious mixing decreases with resolution is generally false. {I}n a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. {A}t finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. {T}he solution to this problem requires a specifically designed advection scheme. {W}e propose and validate the {RSUP}3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the {P}eclet constraint. {T}he rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. {R}ealistic model experiments in a southwest {P}acific configuration show that {RSUP}3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. {T}here are residual errors from the rotated diffusion operator, but they remain acceptable. {T}he use of a constant diffusivity rather than the {P}eclet hyperdiffusivity tends to increase these residual errors which become unacceptable with {L}aplacian diffusion. {F}inally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. {A} temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper.},
  keywords = {{D}iapycnal mixing ; {A}dvection schemes ; {T}errain-following coordinates},
  booktitle = {},
  journal = {{O}cean {M}odelling},
  volume = {26},
  numero = {3-4},
  pages = {156--169},
  ISSN = {1463-5003},
  year = {2009},
  DOI = {10.1016/j.ocemod.2008.09.004},
  URL = {https://www.documentation.ird.fr/hor/fdi:010044261},
}