Frontal waves — tank experiment
In the rotating tank, we will attempt to observe frontal waves by generating a shear
layer. We immerse a disk slightly below the water surface and then rotate it at a speed
δΩ relative to the tank.
delta omega
Omega
You might expect the fluid under the disk to be in solidy body rotation with a rotation
rate δΩ/2 or vorticity δΩ and the fluid outside to have zero vorticity (relative to the tank,
of course). Find the solution with continuous velocity. This is called the Rankine vortex,
and it is stable. In fact, however, you develop shear layers at the edge of the disk (c.f.
Greenspan), and these can become unstable give rise to waves and vortices around the
tank.
Examine the structures as you vary δΩ. The wavelength for the instability should be
roughly 2π times the shear layer width.