Streamplot in a longitudinal section with matplotlib

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I have a spherical shell simulation and would like to plot a longitudinal slice like below showing the streamlines.

Meridional section with streamlines

The dashed and solid lines shown here have been plotted with matplotlib using the contours of the streamfunction obtained from the radial and angular velocities, vr and vtheta. However, I would like to achieve the same using streamplot. Could someone guide me towards how this would be possible?

Thanks!

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