.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_10_gustafson_kullenberg_inertial_oscillations.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_10_gustafson_kullenberg_inertial_oscillations.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_10_gustafson_kullenberg_inertial_oscillations.py:


Gustafson and Kullenberg's inertial oscillations (1936)
=======================================================

Torsten Gustafson and Börje Kullenberg moored current meters in the Baltic
off Gotland and found currents turning clockwise with a period of about 14
hours. That is the inertial period ``2 pi / f`` at 57.8 N: once the wind
stops, water keeps moving and the Coriolis force turns it in circles that
friction slowly damps.

.. GENERATED FROM PYTHON SOURCE LINES 11-38



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_10_gustafson_kullenberg_inertial_oscillations_001.png
   :alt: Inertial period 14.1 h, Clockwise, slowly damped
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_10_gustafson_kullenberg_inertial_oscillations_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.oceanography import inertial_period, simulate_inertial_current

    f = coriolis_parameter(np.radians(57.8))
    period = inertial_period(f)
    assert np.isclose(period / 3600, 14.2, atol=0.1)

    time = np.linspace(0, 5 * 86400, 2001)
    result = simulate_inertial_current(f, time, east_speed=0.3, damping=2e-6)
    east = result.values[:, 0]
    upward = np.flatnonzero((east[:-1] < 0) & (east[1:] >= 0))
    assert np.isclose(np.mean(np.diff(time[upward])), period, rtol=0.01)
    assert result.values[1, 1] < 0  # clockwise: an eastward current first turns south

    fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4))
    left.plot(time / 3600, result.values, label=["east", "north"])
    left.set(xlabel="time [hours]", ylabel="velocity [m/s]", title=f"Inertial period {period / 3600:.1f} h")
    left.legend()
    right.plot(*result.values.T)
    right.set(xlabel="east velocity [m/s]", ylabel="north velocity [m/s]", aspect="equal", title="Clockwise, slowly damped")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.318 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_10_gustafson_kullenberg_inertial_oscillations.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_10_gustafson_kullenberg_inertial_oscillations.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_10_gustafson_kullenberg_inertial_oscillations.ipynb <plot_10_gustafson_kullenberg_inertial_oscillations.ipynb>`

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

      :download:`Download Python source code: plot_10_gustafson_kullenberg_inertial_oscillations.py <plot_10_gustafson_kullenberg_inertial_oscillations.py>`

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

      :download:`Download zipped: plot_10_gustafson_kullenberg_inertial_oscillations.zip <plot_10_gustafson_kullenberg_inertial_oscillations.zip>`


.. only:: html

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

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