Parameterisation of Eddies in Coarse Resolution Models
Abstract
Some requirements on eddy parameterisation are discussed, especially the implications of expressing them in terms of the quasi-Stokes velocity and the modified mean, rather than Eulerian mean, density. The difference between the two means is second-order in perturbation amplitude and thus small in the fluid interior (where formulae to connect the two exist). Near horizontal boundaries, the differences become first order, and so more severe. Existing formulae for quasi-Stokes velocities and stream function also break down here. The layer in which the largest differences between the two mean densities occur is the vertical excursion of a mean isopycnal across a deformation radius, at most about 20 m thick. Most climate models would have difficulty in resolving such a layer. It is shown that extant parameterisation appear to reproduce the Eulerian, and not modified mean, density field and so do not yield a narrow layer at surface and floor either. Both these features make the quasi-Stokes stream function appear to be non-zero right up to rigid boundaries, so that we must query what are the relevant surface and floor quasi-Stokes stream function conditions, and what are their effects on the density fields. To answer this, a variety of eddy parameterisation is employed for a channel problem, and the time-mean density is compared with that from an eddy-resolving calculation. The parameterization were only successful if the vertical component of the quasi- Stokes velocity vanished at top and bottom as in current practice, but all were almost equally successful given proper tuning. One parameterisation, based on linear instability theory, is extended to a global geometry. In low and mid-latitudes, because the predominant orientation of the instability wavevector is north-south, the main quasi-Stokes flow is east-west, only becoming the more traditional north-south at higher latitudes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 19, 2001
- Accession Number
- ADP013574
Entities
People
- Peter D. Killworth