.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_07_glen_flow_law.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_glaciology_plot_07_glen_flow_law.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_glaciology_plot_07_glen_flow_law.py:


Glen's flow law (1955)
======================

John Glen loaded cylinders of polycrystalline ice in compression at constant
stress and temperature and measured their steady creep. The strain rate rose
as about the cube of the stress, with a rate factor that grows steeply towards
the melting point. A Glen glacier therefore shears mostly near its bed and
moves almost as a block above it.

.. GENERATED FROM PYTHON SOURCE LINES 11-36



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_07_glen_flow_law_001.png
   :alt: Glen: strain rate as stress cubed, Higher n: shear concentrates at the bed
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_07_glen_flow_law_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY, ICE_DENSITY
    from earthsciencekit.glaciology import glen_rate_factor, glen_strain_rate, glen_velocity_profile

    stress = np.logspace(4, 6, 50)
    fig, (left, right) = plt.subplots(1, 2, figsize=(10, 4))
    for celsius in (-30, -10, -2):
        factor = glen_rate_factor(273.15 + celsius, 3.5e-25, 6e4, 263.15)
        rate = glen_strain_rate(stress, factor, 3)
        assert np.isclose(np.polyfit(np.log(stress), np.log(rate), 1)[0], 3)
        left.loglog(stress / 1e3, rate, label=f"{celsius} degC")
    left.set(xlabel="stress [kPa]", ylabel="strain rate [1/s]", title="Glen: strain rate as stress cubed")
    left.legend()
    height = np.linspace(0, 300, 151)
    for n in (1, 3, 5):
        velocity = glen_velocity_profile(height, 300, 0.05, 2.4e-24 * (1e5) ** (3 - n), n, ICE_DENSITY, GRAVITY)
        right.plot(velocity / velocity[-1], height, label=f"n = {n}")
    right.set(xlabel="velocity / surface velocity", ylabel="height above the bed [m]", title="Higher n: shear concentrates at the bed")
    right.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.452 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_07_glen_flow_law.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/glaciology/plot_07_glen_flow_law.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_07_glen_flow_law.ipynb <plot_07_glen_flow_law.ipynb>`

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

      :download:`Download Python source code: plot_07_glen_flow_law.py <plot_07_glen_flow_law.py>`

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

      :download:`Download zipped: plot_07_glen_flow_law.zip <plot_07_glen_flow_law.zip>`


.. only:: html

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

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