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I read somewhere that whirlpools in water will attract each other if they are spinning in opposite direction but will repell eachother if they are spinning in same direction.

How does this exactly work? I know equations of fluid mechanism can be hard to grasp. Is there an intutive way normal people can understand this behavior of fluids? What is the mechanism between whirlpools repelling and attracting each other?

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For liquids that are moving Bernoulli's principle states that

$$P+h\rho g+\frac{1}{2}\rho v^2$$

is constant.

This means that the pressure exerted by a faster flowing liquid is reduced (for the same height).

In the diagram the water at A and C is moving fast, but at B the motion cancels and the speed is slower, so the pressure is greater at B, than at A and C, so they repel when spinning in the same direction.

enter image description here

In the lower half of the diagram, they are spinning in opposite directions, now the water speed at E is higher and the pressure is reduced there, compared to D and F, so they attract.

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    $\begingroup$ Are you sure that it is not the other way round? There are two reasons why I would think that co-rotating vortices attract while counter-rotating vortices repel: 1) There is a fast downward flow at E, and moving the vortices closer forces that flow to accelerate to maintain the upwards flows at D and F. At the same time, the net-zero flow at B allows the two co-rotating vortices to merge into a single vortex. 2) If counter-rotating vortices would attract, they would join, canceling each other out. That's not compatible with energy and angular momentum conservation. $\endgroup$
    – cmaster - reinstate monica
    Commented Sep 19, 2021 at 21:22
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    $\begingroup$ @cmaster-reinstatemonica Regarding your point 2): If their rotations are equal and opposite, then the net angular momentum is already zero even when they're far apart, so conservation of angular momentum holds. Conservation of energy holds, too. Remember that energy can also go into turbulence and thermal molecular motion. $\endgroup$
    – Chiral Anomaly
    Commented Sep 20, 2021 at 1:36
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    $\begingroup$ @ChiralAnomaly Indeed, angular momentum is conserved, I take that point back. Energy is not so easy, as it would require rapid transformation of kinetic energy into heat. However, I must add a third point: 3) There are long lived systems of counter-rotating vortices in air. Two examples are the wake turbulence of airplanes, two large vortices that slowly move downwards for several minutes, and smoke rings. Both consist of a fast moving air volume surrounded by counter-rotating vortices, and are stable for surprisingly long times. And both dissipate rather than collapse into themselves. $\endgroup$
    – cmaster - reinstate monica
    Commented Sep 20, 2021 at 6:31
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    $\begingroup$ Vortex interactions are much more interesting than simple attractions & repulsions. Counter-rotating vortices mostly translate in a direction perpendicular to the line between them, while similarly-rotating vortices tend to rotate around each other. $\endgroup$
    – D. Halsey
    Commented Sep 20, 2021 at 16:12

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