.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/plate_tectonics/plot_06_holmes_mantle_convection.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_plate_tectonics_plot_06_holmes_mantle_convection.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_plate_tectonics_plot_06_holmes_mantle_convection.py:


Holmes's mantle convection (1931)
=================================

Arthur Holmes proposed that radioactive heat drives slow convection in the
mantle, which could carry continents. A layer heated from below convects when
its Rayleigh number exceeds about 10^3. For any plausible mantle viscosity the
whole mantle is far above that threshold.

.. GENERATED FROM PYTHON SOURCE LINES 10-32



.. image-sg:: /api/gallery/plate_tectonics/images/sphx_glr_plot_06_holmes_mantle_convection_001.png
   :alt: The mantle must convect
   :srcset: /api/gallery/plate_tectonics/images/sphx_glr_plot_06_holmes_mantle_convection_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    convection stops only above a viscosity of about 4.8e+25 Pa s






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.plate_tectonics import mantle_rayleigh_number

    viscosity = np.logspace(19, 26, 200)
    rayleigh = mantle_rayleigh_number(3e-5, 4500, GRAVITY, 2500, 2.89e6, 1e-6, viscosity)
    critical = 1708.0
    assert mantle_rayleigh_number(3e-5, 4500, GRAVITY, 2500, 2.89e6, 1e-6, 1e21) > 1e4 * critical
    threshold = viscosity[np.argmin(np.abs(np.log(rayleigh / critical)))]
    print(f"convection stops only above a viscosity of about {threshold:.1e} Pa s")

    fig, ax = plt.subplots()
    ax.loglog(viscosity, rayleigh, label="whole mantle")
    ax.axhline(critical, color="k", ls="--", label="onset (rigid walls)")
    ax.axvspan(1e21, 1e22, color="tab:orange", alpha=0.2, label="mantle viscosity")
    ax.set(xlabel="viscosity [Pa s]", ylabel="Rayleigh number", title="The mantle must convect")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.294 seconds)


.. _sphx_glr_download_api_gallery_plate_tectonics_plot_06_holmes_mantle_convection.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/plate_tectonics/plot_06_holmes_mantle_convection.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_holmes_mantle_convection.ipynb <plot_06_holmes_mantle_convection.ipynb>`

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

      :download:`Download Python source code: plot_06_holmes_mantle_convection.py <plot_06_holmes_mantle_convection.py>`

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

      :download:`Download zipped: plot_06_holmes_mantle_convection.zip <plot_06_holmes_mantle_convection.zip>`


.. only:: html

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

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