pg_utils.pg_model.core

Core utilities: coordinates, fields, quantities and controlling parameters in PG model

Jingtao Min @ ETH-EPM, 09.2023

Module Attributes

x	Spatial and time coordinates (Cartesian)
y	Spatial and time coordinates (Cartesian)
z	Spatial and time coordinates (Cartesian)
t	Spatial and time coordinates (Cartesian)
s	Cylindrical and spherical coordinates
p	Cylindrical and spherical coordinates
r	Cylindrical and spherical coordinates
theta	Cylindrical and spherical coordinates
cyl	Cylindrical coordinate system
sph	Spherical coordinate system
H	Half height as a function of polar radius (symbol)
H_s	Half height as a function of polar radius (expr)
B_vec	Vector magnetic field (cylindrical coordinates)
B_sph	Vector magnetic field (spherical coordinates)
U_vec	Vector velocity field (cylindrical coordinates)
v_e	Equatorial velocity (cylindrical coordinates)
U_sph	Vector velocity field (spherical coordinates)
pgvar	Collection of PG variables
U_pg	Quasi-geostrophic velocity ansatz
B0_vec	Background magnetic field (cylindrical)
B0_sph	Background magnetic field (spherical)
U0_vec	Background velocity field (cylindrical)
U0_sph	Background velocity field (spherical)
pgvar_bg	Collection of background PG fields
b_vec	Perturbation of magnetic field (cylindrical)
b_sph	Perturbation of magnetic field (spherical)
u_vec	Perturbation of velocity field (cylindrical)
u_sph	Perturbation of magnetic field (spherical)
pgvar_ptb	Perturbation of PG fields
cgvar	Collection of conjugate variables
cgvar_bg	Collection of background conjugate quantities
cgvar_ptb	Perturbation in conjugate fields
reduced_var	Reduced system variables
fs_sym	Symmetric integral of radial force
fp_sym	Symmetric integral of azimuthal force
fz_asym	Anti-symmetric integral of axial force
fe_p	Azimuthal force in the equatorial plane
eps	Small quantity for linearization \(\epsilon\)
u_linmap	First-order perturbation map of velocity field
b_linmap	First-order perturbation map of magnetic field
pg_linmap	First-order perturbation map of PG variables
cg_linmap	First-order perturbation map of conjugate variables
force_linmap	First-order perturbation in external forcing

Functions

PG_to_conjugate(pg_comp)	Convert PG collection to conjugate counterparts.
conjugate_to_PG(cg_comp)	Convert conjugate quantities to PG counterparts
map_conjugate_to_pg(cg_comp, pg_comp)	Build a dictionary that maps conjugate quantities to PG quantities
map_pg_to_conjugate(pg_comp, cg_comp)	Build a dictionary that maps PG quantities to their conjugates
pg_ansatz(expr[, formal_vel, PG_Psi])	Replace formal velocity with PG ansatz