.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_11_rossby_adjustment_radius.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_oceanography_plot_11_rossby_adjustment_radius.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

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

.. _sphx_glr_api_gallery_oceanography_plot_11_rossby_adjustment_radius.py:


Rossby's adjustment radius (1938)
=================================

Carl-Gustaf Rossby asked what happens when a disturbance in a rotating fluid
is released. Gravity waves carry the imbalance away, but rotation stops them
after a distance equal to the wave speed divided by ``f``: the deformation
radius. In the stratified ocean the first baroclinic radius is a few tens of
kilometres at mid-latitudes, the size of ocean eddies, and grows toward the
equator.

.. GENERATED FROM PYTHON SOURCE LINES 12-35



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_11_rossby_adjustment_radius_001.png
   :alt: Rossby radius of deformation
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_11_rossby_adjustment_radius_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.atmosphere import coriolis_parameter
    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.oceanography import internal_wave_speed, reduced_gravity, rossby_radius

    buoyancy, depth = 3e-3, 4000.0
    latitude = np.radians(np.linspace(5, 80, 151))
    f = coriolis_parameter(latitude)
    radius = rossby_radius(buoyancy, depth, f)
    np.testing.assert_allclose(radius * f, buoyancy * depth / np.pi)
    assert 20e3 < rossby_radius(buoyancy, depth, coriolis_parameter(np.radians(45))) < 60e3
    two_layer = internal_wave_speed(reduced_gravity(2, 1027, GRAVITY), 500, 3500) / f

    fig, ax = plt.subplots()
    ax.semilogy(np.degrees(latitude), radius / 1e3, label="constant N, first mode")
    ax.semilogy(np.degrees(latitude), two_layer / 1e3, "--", label="two layers, 2 kg/m^3 jump")
    ax.set(xlabel="latitude [degrees]", ylabel="deformation radius [km]", title="Rossby radius of deformation")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.130 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_11_rossby_adjustment_radius.py:

.. only:: html

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

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/oceanography/plot_11_rossby_adjustment_radius.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_11_rossby_adjustment_radius.ipynb <plot_11_rossby_adjustment_radius.ipynb>`

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

      :download:`Download Python source code: plot_11_rossby_adjustment_radius.py <plot_11_rossby_adjustment_radius.py>`

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

      :download:`Download zipped: plot_11_rossby_adjustment_radius.zip <plot_11_rossby_adjustment_radius.zip>`


.. only:: html

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

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