Swirling Action of Water

Try an experiment with a few granules of something that floats and a few granules of something that sinks, using clean water, a stirrer and a saucepan.

I think what you are describing is analogous to a low pressure system in the atmosphere. Or filling the bathtub and pulling the plug.

Things get drawn in due to a gradient, not centripetal force.

The water is also subject to the centripital force so the surface is normal to the resultant apparent gravity. This negates any outward drive so that a floating object follows the current which is, probably, down toward the river bed.

The swirling water can not impart enough energy to any entrained material, air, sand, or rocks, to accelerate it to the outer edges of the whirlpool. Therefore it must move to the center.

An air cyclone likewise concentrates dust and heavy particles to the center to drop out the bottom and clean air exits at the top.

You have a couple of different events happening in the eddy current ("swirl"). Due to shear forces between moving water and still water, the eddies occur. You see this as a circular motion in the water surface, sometimes accompanied by the depression in the center of the eddy. Floating objects are moved by the circular current; the faster the current, the deeper the depression. So, to the floating object, you introduce a sloping water surface. Gravity tends to drag things down, so the floating object moves downhill, toward the center of the eddy. For it to leave the eddy, the momentum of the object has to overcome the pull of gravity. The faster the eddy, the greater the momentum. So, either the object falls into the center, or it climbs up the side of the hole.

Not all swirls carry material to the centre. It only happens while the swirl is being maintained by material being removed from the centre. And the swirl actually slows down the general movement towards the centre, just as you might expect*. Light material on the surface is usually rotating slower than the supporting water, and preferentially goes towards the centre. Heavy material at the bottom also goes towards the centre because it is preferentially slowed. But I believe that any heavy material that was in the body of the vortex would tend to separate to the outside until it got near to the bottom.

*If there were no losses, we might expect the movement towards the centre would stop as the centripetal affect balanced the pressure gradient.

Fyz