.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_06_nye_perfectly_plastic_ice_sheet.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_06_nye_perfectly_plastic_ice_sheet.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_06_nye_perfectly_plastic_ice_sheet.py:


Nye's perfectly plastic ice sheet (1951)
========================================

John Nye noticed that the basal shear stress under glaciers varies little,
between about 50 and 150 kPa, and treated ice as a perfectly plastic solid
that yields at a fixed stress. On a flat bed the ice sheet is then a parabola
whose height depends only on the distance from its margin: an ice sheet 1000
km wide stands about 3.3 km high at its centre, as Greenland and Antarctica
do.

.. GENERATED FROM PYTHON SOURCE LINES 12-31



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_06_nye_perfectly_plastic_ice_sheet_001.png
   :alt: Nye: a plastic ice sheet is a parabola
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_06_nye_perfectly_plastic_ice_sheet_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 nye_plastic_profile

    half_width = 500e3
    x = np.linspace(-half_width, half_width, 1001)
    fig, ax = plt.subplots()
    for stress in (50e3, 100e3, 150e3):
        height = nye_plastic_profile(half_width - np.abs(x), stress, ICE_DENSITY, GRAVITY)
        ax.plot(x / 1e3, height, label=f"yield stress {stress / 1e3:.0f} kPa")
    centre = nye_plastic_profile(half_width, 100e3, ICE_DENSITY, GRAVITY)
    assert 3200 < centre < 3400 and np.isclose(nye_plastic_profile(4 * half_width, 100e3, ICE_DENSITY, GRAVITY), 2 * centre)
    ax.set(xlabel="distance from the centre [km]", ylabel="surface height [m]", title="Nye: a plastic ice sheet is a parabola")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.096 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_06_nye_perfectly_plastic_ice_sheet.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_06_nye_perfectly_plastic_ice_sheet.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_nye_perfectly_plastic_ice_sheet.ipynb <plot_06_nye_perfectly_plastic_ice_sheet.ipynb>`

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

      :download:`Download Python source code: plot_06_nye_perfectly_plastic_ice_sheet.py <plot_06_nye_perfectly_plastic_ice_sheet.py>`

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

      :download:`Download zipped: plot_06_nye_perfectly_plastic_ice_sheet.zip <plot_06_nye_perfectly_plastic_ice_sheet.zip>`


.. only:: html

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

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