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 ofindices
withvalue
multiplied by the sign of the permutation.Parameters:
- indices
- sparse_t
- value