Dr Jorgen Frederiksen (CSIRO Atmospheric Research)

Renormalization theory for two-dimensional turbulence.


Lecture 1. Renormalized closure theory for two-dimensional turbulence.

This lecture will provide an exposition of perturbation theory to
homogeneous turbulence and formal renormalization procedure together
with comparisons of closures with propagator renormalization and either
bare vertex or empirical vertex renormalization with DNS for a range
of Reynolds numbers.

Lecture 2. Renormalized viscosity and stochastic backscatter for
two-dimensional turbulence.

In this lecture we will use closure theory to calculate renormalized
viscosity and stochastic backscatter of subgrid scale eddies needed
for large eddy simulations. The formulation of the renormalized
viscosity and stochastic backscatter from the closure equations at high
resolution will be presented. It will be shown that the renormalization
results in very close agreement between the kinetic energy spectra for
the LES and direct numerical simulations (at higher resolution) at the
scales of the LES for both non-rotating turbulence and differentially
rotating Rossby wave turbulence. This is contrasted with much poorer
comparisons using a number of different ad hoc eddy viscosity
parameterizations in LES. Applications to climate models will be
discussed.