Module inprod_analytic

Inner products between the truncated set of basis functions for the ocean and atmosphere streamfunction fields.

These are partly calculated using the analytical expressions from Cehelsky, P., & Tung, K. K. 87). Theories of multiple equilibria and weather regimes-A critical reexamination. Part II: Baroclinic two-layer models. Journal of the atmospheric sciences, 44(21), 3282-3303, 1987.

Fields

atmos.a a_{i,j} = (F_i, \nabla^2 F_j).
atmos.b b_{i,j,k} = (F_i, J(F_j, \nabla^2 F_k)).
atmos.c c_{i,j} = (F_i, \partial_x F_j).
atmos.d d_{i,j} = (F_i, \nabla^2 \eta_j).
atmos.g g_{i,j,k} = (F_i, J(F_j, F_k)).
atmos.s s_{i,j} = (F_i, \eta_j).
ocean.K K_{i,j} = (\eta_i, \nabla^2 F_j).
ocean.M M_{i,j} = (eta_i, \nabla^2 \eta_j).
ocean.N N_{i,j} = (eta_i, \partial_x \eta_j).
ocean.O O_{i,j,k} = (eta_i, J(\eta_j, \eta_k)).
ocean.C C_{i,j,k} = (\eta_i, J(\eta_j,\nabla^2 \eta_k)).
ocean.W W_{i,j} = (\eta_i, F_j).

Local Functions

permute (a, n, sign) Generate permutations, yielding the in-place permutation and the sign of the permutation.
fill_permutations (indices, sparse_t, value) Fill the (sparse) table tofill using the permutations of indices with value multiplied by the sign of the permutation.


Fields

atmos.a
a_{i,j} = (F_i, \nabla^2 F_j).
atmos.b
b_{i,j,k} = (F_i, J(F_j, \nabla^2 F_k)).
atmos.c
c_{i,j} = (F_i, \partial_x F_j). Beta term for the atmosphere
atmos.d
d_{i,j} = (F_i, \nabla^2 \eta_j). Forcing of the ocean on the atmosphere.
atmos.g
g_{i,j,k} = (F_i, J(F_j, F_k)).
atmos.s
s_{i,j} = (F_i, \eta_j). Forcing (thermal) of the ocean on the atmosphere.
ocean.K
K_{i,j} = (\eta_i, \nabla^2 F_j). Forcing of the atmosphere on the ocean.
ocean.M
M_{i,j} = (eta_i, \nabla^2 \eta_j). Forcing of the ocean fields on the ocean.
ocean.N
N_{i,j} = (eta_i, \partial_x \eta_j). Beta term for the ocean
ocean.O
O_{i,j,k} = (eta_i, J(\eta_j, \eta_k)). Temperature advection term (passive scalar)
ocean.C
C_{i,j,k} = (\eta_i, J(\eta_j,\nabla^2 \eta_k)).
ocean.W
W_{i,j} = (\eta_i, F_j). Short-wave radiative forcing of the ocean.

Local Functions

permute (a, n, sign)
Generate permutations, yielding the in-place permutation and the sign of the permutation.

Parameters:

  • a
  • n
  • sign
fill_permutations (indices, sparse_t, value)
Fill the (sparse) table tofill using the permutations of indices with value multiplied by the sign of the permutation.

Parameters:

  • indices
  • sparse_t
  • value
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