State

class fridom.shallowwater.State(mset: ModelSettings, is_spectral: bool = False, field_list=None)

Bases: StateBase

State vector of the 2D shallow water model.

\[\begin{split}\boldsymbol{z} = \begin{pmatrix} u \\ v \\ p \end{pmatrix}\end{split}\]

where \(u\) and \(v\) are the velocity components in the x- and y-directions, and \(p=g\eta\) is the pressure field, with \(\eta\) the free surface elevation.

__init__(mset: ModelSettings, is_spectral: bool = False, field_list=None) → None

Methods

__init__(mset[, is_spectral, field_list])
dot(other)	Calculate the dot product of the state with another state.
fft([padding])	Calculate the Fourier transform of the state.
from_netcdf(mset, path)	Read the state from a NetCDF file.
has_nan()	Check if the state contains NaN values.
ifft([padding])	Calculate the inverse Fourier transform of the state.
norm_l2()	Calculate the L2 norm of the state.
norm_of_diff(other)	The norm of the difference between two states.
project(p_vec, q_vec)	Project the state on a (spectral) vector.
sync()	Synchronize the state.
to_netcdf(path)	Write the state to a NetCDF file.

Attributes

arr_dict	Return the dictionary of arrays (not FieldVariables).
cfl	The CFL number.
ekin	Vertically integrated kinetic energy
epot	Vertically integrated kinetic energy
etot	The total energy
field_list	Return the list of fields.
grid	Return the grid of the model.
local_Ro	Local Rossby number
p	Pressure \(p = g \eta\), where \(\eta\) is the free surface elevation.
pot_vort	Scaled potential vorticity field.
rel_vort	Relative vorticity
u	Velocity in the x-direction.
v	Velocity in the y-direction.
xr	State as xarray dataset
xrs	State of sliced domain as xarray dataset

Examples using fridom.shallowwater.State

Barotropic Instability

Barotropic Instability

property u: FieldVariable

Velocity in the x-direction.

property v: FieldVariable

Velocity in the y-direction.

property p: FieldVariable

Pressure \(p = g \eta\), where \(\eta\) is the free surface elevation.

property ekin: FieldVariable

Vertically integrated kinetic energy

\[E_{\text{kin}} = \frac{Ro^2}{2} h_{\text{full}} (u^2 + v^2)\]

with

\[h_{\text{full}} = c^2 + Ro p\]

Note:

The energy is scaled with the gravity acceleration g.

property epot: FieldVariable

Vertically integrated kinetic energy

\[E_{\text{pot}} = \frac{1}{2} h_{\text{full}}^2\]

with

\[h_{\text{full}} = c^2 + Ro p\]

Note:

The energy is scaled with the gravity acceleration g.

property etot: FieldVariable

The total energy

\[E_{tot} = E_{kin} + E_{pot}\]

property rel_vort: FieldVariable

Relative vorticity

\[\zeta = \partial_x v - \partial_y u\]

property pot_vort: FieldVariable

Scaled potential vorticity field.

\[Q = \frac{\zeta + f \right}{c^2 + Ro p}\]

where \(f\) is the Coriolis parameter, and \(\zeta\) is the relative vorticity.

property local_Ro: FieldVariable

Local Rossby number

\[Ro_\text{local} = Ro \, \frac{\zeta_z}{f_0}\]

where \(Ro\) is the Rossby number, \(\zeta_z\) is the vertical component of the relative vorticity, and \(f_0\) is the Coriolis parameter.

property cfl: FieldVariable

The CFL number.

\[CFL = \max \left\{ \frac{u}{\Delta x}, \frac{v}{\Delta y} \right\} \Delta t\]

where \(\Delta t\) is the time step and \(\Delta x\) is the grid spacing.