Jet

class fridom.shallowwater.initial_conditions.jet.Jet(mset: ModelSettings, wavenum: int = 2, waveamp: float = 0.1, pos: float = 0.5, width: float = 0.1, geo_proj: bool = True)

Bases: State

Two opposing instable jets.

Description

An instable jet setup with a small pressure perturbation on top of it. The jet is given by:

\[u = \exp\left(-\left(\frac{y - p L_y}{\sigma L_y}\right)^2\right)\]

where \(L_y\) is the domain length in the y-direction, \(p\) is the relative position of the jet and \(\sigma\) is the relative width of the jet. The perturbation is given by:

\[p = A \sin \left( \frac{2 \pi}{L_x} k_p x \right)\]

where \(A\) is the amplitude of the perturbation and \(k_p\) is the wavenumber of the perturbation. When geo_proj is set to True, the initial condition is projected to the geostrophic subspace using the geostrophic eigenvectors.

Parameters

msetModelSettings

The model settings.

wavenumint

The relative wavenumber of the perturbation.

waveampfloat

The amplitude of the perturbation.

posfloat

The relative position of the jet in the y-direction

widthfloat

The relative width of the jet.

geo_projbool

Whether to project the initial condition to the geostrophic subspace.

__init__(mset: ModelSettings, wavenum: int = 2, waveamp: float = 0.1, pos: float = 0.5, width: float = 0.1, geo_proj: bool = True)

Methods

__init__(mset[, wavenum, waveamp, pos, ...])
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.initial_conditions.Jet

Barotropic Instability

Barotropic Instability