KelvinWave

class fridom.nonhydro.initial_conditions.kelvin_wave.KelvinWave(mset: ModelSettings, side: str, kz: int, k_parallel: int, phase: float = 0)

Bases: State

Initial condition with a kelvin wave at the boundary.

TODO: Add some more details about the math, add proper gallery example.

Description

Lets consider a Kelvin wave at the southern boundary of the domain with the horizontal wavenumber kh and the vertical wavenumber kz. Searching in the linearized nonhydrostatic equations for a solution of the form:

\[(U, V, W, B) \exp(- k_n y) \exp(i(k_h x + k_z z - \omega t))\]

yields

\[\omega = \sqrt{\frac{k_h^2 N^2}{k_h^2 + k_z^2}} \quad k_n = \frac{k_h f_0}{\omega}\]

\[U = - k_z \quad V = 0 \quad W = k_h \quad B = -i N^2 k_h / \omega\]

Similar polarizations can be found for the other boundaries.

Parameters

msetModelSettings

The model settings object.

sidestr

The side of the domain where the wave is located. Possible values are ‘N’: North, ‘S’: South, ‘E’: East, ‘W’: West.

kzint

The vertical wavenumber. (Can be positive or negative)

khint

The horizontal wavenumber in the direction of the boundary. (Must be positive)

Examples

import fridom.nonhydro as nh
import numpy as np
grid = nh.grid.cartesian.Grid(
    N=[128]*3, L=[1]*3, periodic_bounds=(True, False, True))
mset = nh.ModelSettings(grid=grid)
mset.time_stepper.dt = np.timedelta64(10, 'ms')
mset.tendencies.advection.disable()
mset.setup()
z = nh.initial_conditions.KelvinWave(mset, 'N', kh=1, kz=2)
model = nh.Model(mset)
model.z = z
model.run(runlen=np.timedelta64(5, 's'))

A vertical mode may be constructed with

z  = nh.initial_conditions.kelvin_wave(mset, 'N', kh=1, kz=2)
z += nh.initial_conditions.kelvin_wave(mset, 'N', kh=1, kz=-2, phase=np.pi)

__init__(mset: ModelSettings, side: str, kz: int, k_parallel: int, phase: float = 0)

Methods

__init__(mset, side, kz, k_parallel[, phase])
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).
b	Buoyancy
cfl	The CFL number.
ekin	The kinetic energy
epot	The potential energy
etot	The total energy
field_list	Return the list of fields.
grid	Return the grid of the model.
linear_pot_vort	Linearized potential vorticity
local_Ro	Local Rossby number
pot_vort	Scaled potential vorticity field.
rel_vort	The relative vorticity
rel_vort_x	X-component of the relative vorticity
rel_vort_y	Y-component of the relative vorticity
rel_vort_z	Z-component of the relative vorticity (Horizontal Vorticity)
u	Velocity in the x-direction.
v	Velocity in the y-direction.
w	Velocity in the z-direction.
xr	State as xarray dataset
xrs	State of sliced domain as xarray dataset