README
Package: dss_beta_plane
URL: https://bitbucket.org/kburns/dss_beta_plane
Author: Keaton J. Burns
Overview
This package implements a direct statistical simulation (DSS) of barotropic beta-plane dynamics under a zonal average using Dedalus.
The equation set is based on the form presented in Tobias & Marston 2013: http://adsabs.harvard.edu/abs/2013PhRvL.110j4502T
Implementation
The Dedalus implementation solves for the first and second streamfunction cumulants over a 3D domain (x, y0, y1)
, with y
in [a,b]
, analogous to (ξ, y, y')
in the reference notation.
One dimensional functions, such as the first cumulant, are stored in a 'diagonal' representation in (y0, y1)
. That is, a 1D function c(z)
would be stored as a 3D Dedalus field C
such that,
C(x, y0, y1) = c(y0+y1-a)
In terms of Fourier coefficients,
<kx, ky0, ky1 | C> = δ(kx, 0) * δ(ky0, ky1) * <ky0 | c(y0)>
This representation allows C
to be utilized as a 1D function of either y0
or y1
simply by interpolation at y1=a
or y0=a
, respectively.
An operator called FourierDiagonal
implements spectral interpolation along the diagonal of a bivariate Fourier series, and is used to extract the local part of the second cumulant, which is then stored in the diagonal format described above. I.e. for g = Diag(f)
,
g(x, y0, y1) = f(x, y0+y1-a, y0+y1-a)