Imagine that you partially fill a horizontal cylinder with a viscous fluid, like corn syrup or honey. If that cylinder is still, the fluid will simply pool along the bottom. On the opposite extreme, if you spin it very fast, that cylinder will become coated in an even layer of fluid that rotates along with the cylinder thanks to centrifugal force. Between those two extremes in rotational velocity, some interesting fluid behaviors occur. Start spinning the cylinder and some of the pooled fluid will be pulled up the sides, eventually forming a thicker film with a straight front along the bottom of the cylinder. Spin faster and that straight front starts to break down, forming sharper cusp-like waves known as shark teeth. (Image credit: S. Morris et al., source; research credit: S. Thoroddsen and L. Mahadevan)
Tag: free surface
Typhoon Neoguri
Astronaut Reid Wiseman has been posting photos of Typhoon Neoguri in his Twitter feed this week. From our perspective on the ground, it’s easy to forget how three-dimensional the typhoons and hurricanes in our atmosphere are. But Wiseman’s photos capture the depth in the storm, especially the depression of the eye. From the top, the typhoon looks much like a vortex in a bathtub, or what’s more formally known as a free surface vortex. To understand why a vortex dips in the middle, imagine a container of water on a rotating plate. As the water is spun, its interface with the air takes on a paraboloid shape. Two external forces are acting on the fluid: gravity in the downward direction and a centrifugal force in the radial direction. The free surface of the fluid adopts a shape that is always perpendicular to the combination of these two forces. This ensures that the pressure along the free surface is a constant. (Photo credits: R. Wiseman 1,2,3)
Spinning Polygons
Nature is full of surprising behaviors. If one imagines putting a bucket of water on a rotating plate and spinning it, one would expect the water’s free surface to take on a curved, axially symmetric shape. The photos above are from a similar experiment, but instead of the entire container rotating, only the bottom plate spins. Surprisingly, the water’s surface does not remain symmetric around the axis of rotation. Instead, the water forms stable polygon shapes that rotate slower than the spinning plate. As the plate’s rotation speed increases, the number of corners in the polygon increases. Shapes up to a hexagon were observed in the experiment. Photos of the set-up and more experimental results are available, as is the original research paper. Symmetry breaking and polygons can also be found in hydraulic jumps and bumps, liquid sheets, and planetary polar vortices. (Photo credit: T. Jansson et al.; research paper)
Shark-Tooth Instability
A viscous fluid inside a horizontally rotating circular cylinder forms a shark-tooth-like pattern along the fluid’s free surface. This is one of several patterns observed depending on the fluid’s viscosity and surface tension and the rotational rate of the cylinder. (Photo credit: S. Thoroddsen and L. Mahadevan; for more, see Thoroddsen and Mahadevan 1996 and 1997)
