Why does gravity cause secondary flow in pipes?

[Wiemster]

In a straight pipe flow, secondary flow patterns (i.e. perpendicular to the axis of the pipe) arise due to gravity in the form of two counterrotating vortices (or so I heard).

But why is the dynamics at all changed in the presence of a gravitational field? Why isn't the pressure just modified in such a way that gravity is effectively cancelled? Gravity is a conservative force after all, so can be written as the gradient of a scalar field. Why isn't this scalar field just added to the pressure, resulting in a modified pressure, leaving the dynamics unchanged?

Is this a stability issue, with the sketched scenario possible, but unstable?

 

[Achy47]

Thank you for your question about the dynamics of secondary flow patterns in straight pipe flow. You are correct that the presence of a gravitational field does change the dynamics of the flow. This is due to a phenomenon known as the Coriolis effect.

The Coriolis effect is an inertial force that arises due to the rotation of the Earth. In the case of straight pipe flow, the Coriolis effect causes the fluid particles to experience a force perpendicular to their direction of motion. This results in the formation of the two counterrotating vortices that you mentioned.

It is true that gravity is a conservative force and can be written as the gradient of a scalar field. However, in the case of the Coriolis effect, the force is not directly due to gravity, but rather the rotation of the Earth. Therefore, simply adding a scalar field to the pressure would not cancel out the effects of the Coriolis force.

In terms of stability, the formation of secondary flow patterns in straight pipe flow is a stable phenomenon. However, there are certain conditions in which the flow can become unstable and lead to chaotic flow patterns. This is known as transitional flow and is an active area of research in fluid dynamics.

I hope this explanation helps to clarify the role of the Coriolis effect in secondary flow patterns in straight pipe flow. If you have any further questions, please don't hesitate to ask.