.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_15_munk_abyssal_recipes.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_oceanography_plot_15_munk_abyssal_recipes.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_oceanography_plot_15_munk_abyssal_recipes.py:


Munk's abyssal recipes (1966)
=============================

Walter Munk noticed that the deep Pacific temperature profile is exponential
with a scale of about 1 km. Cold water sinking near Antarctica must upwell
through the abyss, and the upwelling ``w`` and downward mixing ``kappa``
balance when ``h = kappa / w``. With ``w`` about 1.2 cm per day the profile
needs a diffusivity of about 1e-4 m^2/s, far more than measured in the
interior, a puzzle that took 30 years to resolve.

.. GENERATED FROM PYTHON SOURCE LINES 12-40



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_15_munk_abyssal_recipes_001.png
   :alt: Scale height 936 m, Stratification of the abyss
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_15_munk_abyssal_recipes_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.oceanography import abyssal_temperature, buoyancy_frequency_squared, linear_density
    from earthsciencekit.units import convert

    diffusivity, upwelling, column = 1.3e-4, 1.2e-2 / 86400, 3000.0
    height = np.linspace(0, column, 3001)
    temperature = abyssal_temperature(height, convert(1.0, "degC", "K"), convert(5.0, "degC", "K"), column, diffusivity, upwelling)
    gradient = np.gradient(temperature, height)
    scale = 1 / np.polyfit(height[10:-10], np.log(gradient[10:-10]), 1)[0]
    assert np.isclose(scale, diffusivity / upwelling, rtol=1e-3)

    density = linear_density(1027, temperature - temperature[0], 0, 2e-4, 7.6e-4)
    n2 = buoyancy_frequency_squared(density, np.gradient(density, height), GRAVITY)
    assert np.all(n2 > 0)

    fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4), sharey=True)
    left.plot(convert(temperature, "K", "degC"), (column - height) / 1e3 + 1)
    left.set(xlabel="temperature [degC]", ylabel="depth [km]", title=f"Scale height {scale:.0f} m")
    left.invert_yaxis()
    right.plot(np.sqrt(n2) * 1e3, (column - height) / 1e3 + 1)
    right.set(xlabel="buoyancy frequency N [10^-3 1/s]", title="Stratification of the abyss")
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.166 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_15_munk_abyssal_recipes.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/oceanography/plot_15_munk_abyssal_recipes.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_15_munk_abyssal_recipes.ipynb <plot_15_munk_abyssal_recipes.ipynb>`

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

      :download:`Download Python source code: plot_15_munk_abyssal_recipes.py <plot_15_munk_abyssal_recipes.py>`

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

      :download:`Download zipped: plot_15_munk_abyssal_recipes.zip <plot_15_munk_abyssal_recipes.zip>`


.. only:: html

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

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