CoherentEddy

class fridom.nonhydro.initial_conditions.coherent_eddy.CoherentEddy(mset: ModelSettings, pos_x: float = 0.5, pos_y: float = 0.5, width: float = 0.1, amplitude: float = 1, gauss_field: str = 'streamfunction')

Bases: State

Coherent barotropic eddy with Gaussian shape.

Description

There are two versions of the coherent eddy. In the first version, the streamfunction of the eddy is given by an gaussian function:

\[\psi = A \exp\left( -\frac{(x - p_x L_x)^2 + (y - p_y L_y)^2}{(\sigma L_x)^2}\right)\]

where \(A\) is the amplitude, \((p_x, p_y)\) is the relative position of the eddy, \((\sigma L_x)\) is the width of the eddy, and \(L_x, L_y\) are the domain sizes in the x and y directions. The velocity field is given by:

\[u = \partial_y \psi, \quad v = -\partial_x \psi\]

The second version of the coherent eddy prescribes the horizontal velocity as a gaussian function:

\[\zeta = A \exp\left( -\frac{(x - p_x L_x)^2 + (y - p_y L_y)^2}{(\sigma L_x)^2}\right)\]

Then the streamfunction is computed in spectral space:

\[\hat{\psi} = \frac{\hat{\zeta}}{k_x^2 + k_y^2}\]

Parameters

msetModelSettings

The model settings.

pos_xfloat, optional (default=0.5)

The relative position of the eddy in the x-direction.

pos_yfloat, optional (default=0.5)

The relative position of the eddy in the y-direction.

widthfloat, optional (default=0.1)

The relative width of the eddy. (relative to the domain size in the x-direction)

amplitudefloat, optional (default=1)

The amplitude of the eddy. When the amplitude negative, the eddy rotates clockwise. Otherwise, it rotates counterclockwise.

gauss_fieldstr, optional (default=’vorticity’)

The field that is prescribed as a gaussian function. It can be either ‘vorticity’ or ‘streamfunction’.

Examples

This setup creates a coherent eddy in an scaled setup with varying coriolis parameter. The eddy moves in positive x and negative y direction and hits the northern wall.

import fridom.nonhydro as nh
import numpy as np
grid = nh.grid.cartesian.Grid(
    N=(128, 128, 1), L=(3, 3, 1), periodic_bounds=(True, False, False))
mset = nh.ModelSettings(grid=grid, f0=1, beta=0.2)
mset.time_stepper.dt = 0.004
mset.setup()
model = nh.Model(mset)
model.z = nh.initial_conditions.CoherentEddy(mset, width=0.15)
model.run(runlen=np.timedelta64(20, 's'))

The eddy becomes a rossby wave when either the amplitude is very small or the advection term is disabled:

mset.tendencies.advection.disable()

__init__(mset: ModelSettings, pos_x: float = 0.5, pos_y: float = 0.5, width: float = 0.1, amplitude: float = 1, gauss_field: str = 'streamfunction') → None

Methods

__init__(mset[, pos_x, pos_y, width, ...])
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

Examples using fridom.nonhydro.initial_conditions.CoherentEddy

Dancing Eddies

Dancing Eddies

Tracers and Eddies

Tracers and Eddies