.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/oceanography/plot_12_sverdrup_balance.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_12_sverdrup_balance.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_12_sverdrup_balance.py:


Sverdrup's balance (1947)
=========================

Harald Sverdrup showed that in the ocean interior the curl of the wind stress
is balanced by flow across lines of latitude, where the planetary vorticity
changes at the rate beta. Under the westerlies and trade winds of a
subtropical gyre the whole interior drifts equatorward by tens of Sverdrups,
and a narrow current on one boundary must carry it back.

.. GENERATED FROM PYTHON SOURCE LINES 11-38



.. image-sg:: /api/gallery/oceanography/images/sphx_glr_plot_12_sverdrup_balance_001.png
   :alt: Sverdrup transport across a 6000 km basin
   :srcset: /api/gallery/oceanography/images/sphx_glr_plot_12_sverdrup_balance_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    a 100 km wide, 1000 m deep boundary current must flow at 0.28 m/s






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import EARTH_RADIUS, OMEGA_EARTH
    from earthsciencekit.oceanography import sverdrup_transport, volume_transport
    from earthsciencekit.units import convert

    stress, width, south, north = 0.1, 6000e3, np.radians(15), np.radians(45)
    length = EARTH_RADIUS * (north - south)
    latitude = np.linspace(south, north, 121)
    y = EARTH_RADIUS * (latitude - south)
    curl = -stress * np.pi / length * np.sin(np.pi * y / length)
    beta = 2 * OMEGA_EARTH * np.cos(latitude) / EARTH_RADIUS
    interior = convert(sverdrup_transport(curl, 1025, beta) * width, "m^3/s", "Sv")
    assert -60 < interior.min() < -10

    return_speed = -interior.min() * 1e6 / (100e3 * 1000)
    assert np.isclose(convert(volume_transport(return_speed, 100e3, 1000), "m^3/s", "Sv"), -interior.min())
    print(f"a 100 km wide, 1000 m deep boundary current must flow at {return_speed:.2f} m/s")

    fig, ax = plt.subplots()
    ax.plot(interior, np.degrees(latitude))
    ax.axvline(0, color="k", lw=0.5)
    ax.set(xlabel="interior northward transport [Sv]", ylabel="latitude [degrees]", title="Sverdrup transport across a 6000 km basin")

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.072 seconds)


.. _sphx_glr_download_api_gallery_oceanography_plot_12_sverdrup_balance.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_12_sverdrup_balance.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_12_sverdrup_balance.ipynb <plot_12_sverdrup_balance.ipynb>`

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

      :download:`Download Python source code: plot_12_sverdrup_balance.py <plot_12_sverdrup_balance.py>`

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

      :download:`Download zipped: plot_12_sverdrup_balance.zip <plot_12_sverdrup_balance.zip>`


.. only:: html

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

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