.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_16_wilson_head_dike_ascent.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_16_wilson_head_dike_ascent.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_16_wilson_head_dike_ascent.py:


Wilson and Head's magma ascent in dikes (1981)
==============================================

Lionel Wilson and James Head followed magma up dikes from its source to the
surface on the Earth and the Moon. Buoyancy drives laminar flow between the
walls at a speed that grows as the square of the width, and the magma's
dissolved water comes out of solution as the pressure falls. Basalt in a dike
a metre wide rises at metres per second; a viscous rhyolite barely moves.

.. GENERATED FROM PYTHON SOURCE LINES 11-42



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_16_wilson_head_dike_ascent_001.png
   :alt: Speed grows as width squared, Water exsolves on the way up
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_16_wilson_head_dike_ascent_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.volcanology import dike_ascent_velocity, water_solubility

    width = np.logspace(-1, 1, 100)
    magmas = {"basalt, 100 Pa s": 100.0, "andesite, 1e5 Pa s": 1e5, "rhyolite, 1e8 Pa s": 1e8}
    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    for name, viscosity in magmas.items():
        left.loglog(width, dike_ascent_velocity(width, 300, viscosity, GRAVITY), label=name)
    speed = dike_ascent_velocity(1.0, 300, 100, GRAVITY)
    assert 2700 * speed * 1.0 / 100 < 2000  # laminar
    left.set(xlabel="dike width [m]", ylabel="ascent speed [m/s]", title="Speed grows as width squared")
    left.legend(fontsize=8)

    depth = np.linspace(0, 8000, 400)
    pressure = 2400 * GRAVITY * depth
    dissolved = water_solubility(pressure, 4.1e-6)
    saturation = (0.05 / 4.1e-6) ** 2 / (2400 * GRAVITY)
    assert np.isclose(water_solubility(2400 * GRAVITY * saturation, 4.1e-6), 0.05)
    right.plot(100 * dissolved, depth / 1e3, label="solubility")
    right.axvline(5, color="0.5", ls="--", label="magma with 5 wt% water")
    right.axhline(saturation / 1e3, color="C3", lw=1, label=f"bubbles from {saturation / 1e3:.1f} km")
    right.invert_yaxis()
    right.set(xlabel="dissolved water [wt%]", ylabel="depth [km]", title="Water exsolves on the way up")
    right.legend(fontsize=8)
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.299 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_16_wilson_head_dike_ascent.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_16_wilson_head_dike_ascent.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_16_wilson_head_dike_ascent.ipynb <plot_16_wilson_head_dike_ascent.ipynb>`

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

      :download:`Download Python source code: plot_16_wilson_head_dike_ascent.py <plot_16_wilson_head_dike_ascent.py>`

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

      :download:`Download zipped: plot_16_wilson_head_dike_ascent.zip <plot_16_wilson_head_dike_ascent.zip>`


.. only:: html

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

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