.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_15_wilson_sparks_eruption_columns.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_volcanology_plot_15_wilson_sparks_eruption_columns.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_volcanology_plot_15_wilson_sparks_eruption_columns.py:


Wilson, Sparks, Huang and Watkins's eruption columns (1978)
===========================================================

Wilson, Sparks, Huang and Watkins treated a Plinian eruption column as a
buoyant plume driven by the heat of its fragmented magma. Its height grows as
the fourth root of the heat flux, about ``8.2 Q**(1/4)`` metres, so a column
ten times higher needs ten thousand times the eruption rate. The same height
follows from the Morton-Taylor-Turner plume with the buoyancy flux of that
heat in the atmosphere.

.. GENERATED FROM PYTHON SOURCE LINES 12-34



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_15_wilson_sparks_eruption_columns_001.png
   :alt: Height grows as the fourth root of heat flux
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_15_wilson_sparks_eruption_columns_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import CP_DRY_AIR, GRAVITY
    from earthsciencekit.volcanology import column_height, plume_rise_height

    rate = np.logspace(3, 9, 61)  # kg/s of magma
    heat = rate * 1100 * 1000  # specific heat 1100 J/(kg K), cooled by 1000 K
    height = column_height(heat)
    buoyancy_flux = GRAVITY * heat / (1.1 * CP_DRY_AIR * 270) / np.pi  # air 1.1 kg/m^3 at 270 K
    plume = plume_rise_height(buoyancy_flux, 0.01)
    assert np.allclose(height / plume, height[0] / plume[0]) and abs(height[0] / plume[0] - 1) < 0.15
    assert np.isclose(column_height(1e12), 8200)

    fig, ax = plt.subplots()
    ax.loglog(rate, height / 1e3, label="8.2 Q^(1/4)")
    ax.loglog(rate, plume / 1e3, "--", label="MTT plume, N = 0.01 1/s")
    ax.set(xlabel="mass eruption rate [kg/s]", ylabel="column height [km]", title="Height grows as the fourth root of heat flux")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.223 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_15_wilson_sparks_eruption_columns.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/volcanology/plot_15_wilson_sparks_eruption_columns.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_15_wilson_sparks_eruption_columns.ipynb <plot_15_wilson_sparks_eruption_columns.ipynb>`

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

      :download:`Download Python source code: plot_15_wilson_sparks_eruption_columns.py <plot_15_wilson_sparks_eruption_columns.py>`

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

      :download:`Download zipped: plot_15_wilson_sparks_eruption_columns.zip <plot_15_wilson_sparks_eruption_columns.zip>`


.. only:: html

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

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