.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_04_stokes_deep_water_waves.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_04_stokes_deep_water_waves.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_04_stokes_deep_water_waves.py:


Stokes's deep-water waves (1847)
================================

George Gabriel Stokes worked out oscillatory waves of small and finite height.
The dispersion relation ``omega**2 = g k tanh(k h)`` makes long waves travel
faster than short ones. In deep water the energy travels at the group speed,
half the speed of the crests, which is why the swell from a distant storm
arrives longest waves first.

.. GENERATED FROM PYTHON SOURCE LINES 11-37



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_04_stokes_deep_water_waves_001.png
   :alt: Dispersion in water 50 m deep
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_04_stokes_deep_water_waves_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.oceanography import deep_group_speed, deep_wave_speed, shallow_wave_speed, wave_angular_frequency

    depth = 50.0
    wavelength = np.logspace(0, 4, 2001)
    k = 2 * np.pi / wavelength
    omega = wave_angular_frequency(k, depth, GRAVITY)
    group = np.gradient(omega, k)
    deep = wavelength < depth
    np.testing.assert_allclose(group[deep][5:-5], deep_group_speed(wavelength[deep][5:-5], GRAVITY), rtol=1e-3)
    np.testing.assert_allclose(deep_group_speed(wavelength, GRAVITY), 0.5 * deep_wave_speed(wavelength, GRAVITY))

    fig, ax = plt.subplots()
    ax.loglog(wavelength, omega / k, label="phase speed")
    ax.loglog(wavelength, group, label="group speed")
    ax.loglog(wavelength, deep_wave_speed(wavelength, GRAVITY), "k--", lw=0.8, label="deep-water limits")
    ax.loglog(wavelength, deep_group_speed(wavelength, GRAVITY), "k--", lw=0.8)
    ax.axhline(shallow_wave_speed(depth, GRAVITY), color="0.5", ls=":", label="shallow-water limit")
    ax.set(xlabel="wavelength [m]", ylabel="speed [m/s]", title=f"Dispersion in water {depth:.0f} m deep")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.175 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_04_stokes_deep_water_waves.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_04_stokes_deep_water_waves.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_stokes_deep_water_waves.ipynb <plot_04_stokes_deep_water_waves.ipynb>`

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

      :download:`Download Python source code: plot_04_stokes_deep_water_waves.py <plot_04_stokes_deep_water_waves.py>`

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

      :download:`Download zipped: plot_04_stokes_deep_water_waves.zip <plot_04_stokes_deep_water_waves.zip>`


.. only:: html

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

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