.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/glaciology/plot_02_forbes_viscous_glacier_flow.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_02_forbes_viscous_glacier_flow.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_02_forbes_viscous_glacier_flow.py:


Forbes's viscous glacier flow (1843)
====================================

James David Forbes surveyed the Mer de Glace and found that its centre moves
faster than its margins, and its surface faster than its depths, with a speed
that changes with the seasons. He concluded that a glacier is "an imperfect
fluid" flowing under its own weight. For a slab of uniform viscosity the
velocity is a parabola in height, and its depth average is two-thirds of the
surface speed.

.. GENERATED FROM PYTHON SOURCE LINES 12-32



.. image-sg:: /api/gallery/glaciology/images/sphx_glr_plot_02_forbes_viscous_glacier_flow_001.png
   :alt: Forbes: a viscous slab, basal stress 144 kPa
   :srcset: /api/gallery/glaciology/images/sphx_glr_plot_02_forbes_viscous_glacier_flow_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, SECONDS_PER_YEAR
    from earthsciencekit.glaciology import driving_stress, viscous_slab_velocity

    thickness, slope = 200.0, 0.08
    height = np.linspace(0, thickness, 201)
    fig, ax = plt.subplots()
    for viscosity in (2e13, 5e13, 1e14):
        velocity = viscous_slab_velocity(height, thickness, slope, viscosity, ICE_DENSITY, GRAVITY)
        mean = np.trapezoid(velocity, height) / thickness
        assert np.isclose(mean, 2 / 3 * velocity[-1], rtol=1e-4)
        ax.plot(velocity * SECONDS_PER_YEAR, height, label=f"viscosity {viscosity:.0e} Pa s")
    stress = driving_stress(thickness, slope, ICE_DENSITY, GRAVITY)
    ax.set(xlabel="velocity [m/year]", ylabel="height above the bed [m]", title=f"Forbes: a viscous slab, basal stress {stress / 1e3:.0f} kPa")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.091 seconds)


.. _sphx_glr_download_api_gallery_glaciology_plot_02_forbes_viscous_glacier_flow.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_02_forbes_viscous_glacier_flow.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_forbes_viscous_glacier_flow.ipynb <plot_02_forbes_viscous_glacier_flow.ipynb>`

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

      :download:`Download Python source code: plot_02_forbes_viscous_glacier_flow.py <plot_02_forbes_viscous_glacier_flow.py>`

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

      :download:`Download zipped: plot_02_forbes_viscous_glacier_flow.zip <plot_02_forbes_viscous_glacier_flow.zip>`


.. only:: html

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

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