.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/elliptic_oecs/plot_bickley_elliptic_oecs.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_elliptic_oecs_plot_bickley_elliptic_oecs.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_elliptic_oecs_plot_bickley_elliptic_oecs.py:


Bickley jet Elliptic OECS
=========================

Compute the IVD-based elliptic OECS for the Bickley jet.

.. GENERATED FROM PYTHON SOURCE LINES 8-18

.. code-block:: Python


    # Author: ajarvis

    import numpy as np
    from math import pi
    import matplotlib.pyplot as plt
    from numbacs.flows import get_predefined_callable
    from numbacs.diagnostics import ivd_grid_2D
    from numbacs.extraction import rotcohvrt
    from numbacs.utils import curl_func_tspan







.. GENERATED FROM PYTHON SOURCE LINES 19-22

Get flow callable
-----------------
Get callable for velocity field, set up domain, and initial time

.. GENERATED FROM PYTHON SOURCE LINES 22-39

.. code-block:: Python


    # retrieve callable to compute vorticity
    vel_spline = get_predefined_callable("bickley_jet", return_domain=False)

    # set up larger domain to capture all elliptic lcs
    domain = ((-2.0, 6.371 * pi + 2.0), (-3.0, 3.0))
    dx = 0.05
    dy = 0.05
    x = np.arange(domain[0][0], domain[0][1] + dx, dx)
    y = np.arange(domain[1][0], domain[1][1] + dy, dy)
    nx = len(x)
    ny = len(y)

    # set initial time
    t0 = 0.0
    t = np.array([t0])








.. GENERATED FROM PYTHON SOURCE LINES 40-43

Vorticity
---------
Compute vorticity on the grid at t0.

.. GENERATED FROM PYTHON SOURCE LINES 43-48

.. code-block:: Python


    # compute vorticity and spatial mean of vorticity
    vort = curl_func_tspan(vel_spline, t, x, y).squeeze()
    vort_avg = np.mean(vort)








.. GENERATED FROM PYTHON SOURCE LINES 49-52

IVD
---
Compute IVD from vorticity.

.. GENERATED FROM PYTHON SOURCE LINES 52-56

.. code-block:: Python


    # compute lavd
    ivd = ivd_grid_2D(vort, vort_avg)








.. GENERATED FROM PYTHON SOURCE LINES 57-60

IVD-based elliptic OECS
-----------------------
Compute elliptic OECS from IVD.

.. GENERATED FROM PYTHON SOURCE LINES 60-66

.. code-block:: Python


    # set parameters and compute lavd-based elliptic oecs
    r = 2.5
    convexity_deficiency = 5e-6
    min_len = 1.0
    elcs = rotcohvrt(ivd, x, y, r, convexity_deficiency=convexity_deficiency, min_len=min_len)







.. GENERATED FROM PYTHON SOURCE LINES 67-70

Plot
----
Plot the elliptic OECS over the IVD field.

.. GENERATED FROM PYTHON SOURCE LINES 70-79

.. code-block:: Python


    # sphinx_gallery_thumbnail_number = 1
    fig, ax = plt.subplots(dpi=200)
    ax.contourf(x, y, ivd.T, levels=80)
    ax.set_aspect("equal")
    for rcv, c in elcs:
        ax.plot(rcv[:, 0], rcv[:, 1], lw=1.5)
        ax.scatter(c[0], c[1], 1.5)
    plt.show()



.. image-sg:: /auto_examples/elliptic_oecs/images/sphx_glr_plot_bickley_elliptic_oecs_001.png
   :alt: plot bickley elliptic oecs
   :srcset: /auto_examples/elliptic_oecs/images/sphx_glr_plot_bickley_elliptic_oecs_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 1.693 seconds)


.. _sphx_glr_download_auto_examples_elliptic_oecs_plot_bickley_elliptic_oecs.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_bickley_elliptic_oecs.ipynb <plot_bickley_elliptic_oecs.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_bickley_elliptic_oecs.py <plot_bickley_elliptic_oecs.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_bickley_elliptic_oecs.zip <plot_bickley_elliptic_oecs.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_