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])
abs()	Map the field by taking the absolute value (\(|f|\)).
apply_elementwise(vector_field, op)	Apply an operation elementwise to the vector field.
apply_water_mask()	Apply a water mask to the field.
conj()	Compute the complex conjugate.
cumulative_integral(axis[, direction])	Compute the cumulative integral along an axis.
diff(axis[, order])	Compute the partial derivative along an axis.
div()	Compute the divergence.
dot(other)	Compute the dot product with another field.
extend(topo)	Extend the field in the specified directions.
fft([padding])	Perform a Fast Fourier Transform (FFT) on the field.
from_netcdf(mset, path)	Create a field from a NetCDF file.
from_xarray(mset, ds)	Create a field from an xarray object.
grad([axes])	Compute the gradient.
has_nan()	Check if the field contains NaN values.
ifft([padding])	Perform an Inverse Fast Fourier Transform (IFFT) on the field.
integrate([axes])	Global integral of the Field in specified axes.
laplacian([axes])	Compute the Laplacian.
max([axes])	Maximum value of the Field over the whole domain.
mean([axes])	Global mean of the Field in specified axes.
min([axes])	Minimum value of the Field over the whole domain.
norm_l2()	Calculate the L2 norm of the field.
norm_of_diff(other)	Norm of difference between two vector fields.
project(p_vec, q_vec)	Project a Vector Field onto a (spectral) vector.
set_random([seed])	Set the field to random values.
sum([axes])	Sum of the Field over the whole domain in the specified axes.
sync()	Synchronize the field across all MPI ranks and apply boundary conditions.
to_netcdf(path)	Save the field to a NetCDF file.

Attributes

b	Buoyancy.
cfl	The CFL number.
ekin	The kinetic energy.
epot	The potential energy.
etot	The total energy.
field_list	The list of scalar fields.
fields	The dictionary of scalar fields.
grid	The grid object.
info	Dictionary with information about the field.
is_constant	Flag indicating whether the field is constant.
is_spectral	Flag indicating whether the field is in spectral space.
linear_pot_vort	Linearized potential vorticity.
local_rossby_number	Local Rossby number.
mset	The model settings.
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).
tracers	The tracer fields.
u	Velocity in the x-direction.
v	Velocity in the y-direction.
vector_dim	The vector dimension.
velocity	The velocity vector field.
w	Velocity in the z-direction.
xr	The xarray representation of the field.
xrs	Convert a slice of the field to an xarray object.