The effects of horizontal diffusion on baroclinic development in a spectral model

Abstract

AbstractLinear and non‐linear effects on baroclinic development of linear horizontal diffusion of the form K▽2q, where q is an integer and k, in general, a constant, are investigated using a spectral model and a climatological wintertime northern hemisphere basic state.An eigenvalue approach shows the greatest linear sensitivity to the diffusion to be in the high zonal wavenumbers (m > 12) which, in the absence of diffusion or with the more scale‐selective formulations (large q), are more unstable than the intermediate wavenumbers (m = 7–9). The ▽4 diffusion with a decay time scale of 6 h on the shortest retained scale, which has traditionally been used in our model, is shown to affect significantly the linear stability of almost all wavenumbers, whereas the more scale‐selective formulations have only a very small effect on m < 12.Without dissipation, integrations exhibit grossly physically unrealistic features after about nine days even with very high resolution, indicating the crucial role played by dissipation in non‐linear baroclinic development. Non‐linear integrations with dissipation show great sensitivity to the formulation used. Typically about three times more energy is converted from potential to kinetic with a ▽6 than with a ▽4 diffusion having a similar decay time scale on the smallest retained spatial scale. It appears that as the dissipation time scale on the large spatial scales is increased while retaining sufficiently short time scales near the truncation limit to prevent the accumulation of energy there, so the amount of potential to kinetic energy conversion approaches a limiting value equal to about five times the energy conversion with the ▽4 diffusion. In the limiting case the amount of energy lost to dissipation is equivalent to about 45% of that converted from potential to kinetic energy, again emphasizing the crucial role played by dissipation.It is found that if the decay time scale on the short spatial scales is too long then the integrations exhibit large truncation dependency. This provides a criterion for judging the suitability of a particular choice of dissipation, which might have quite general applicability.