Storm in a bottle

The contraption shown above forms an airtight seal between two soda bottles, allowing water from one to flow into the other. The flow can start in one of two ways:

  • Flip the system over at \(t=0\) and let gravity pull the water down.
  • Flip the system over at \(t=0\), and give the system a slight twirl, forming a vortex. The center of a vortex is an empty hole through which air can pass.

Which of the two flows will let the water reach the bottom first?

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