**TAYLOR-COUETTE FLOW:
THE CLASSIC DEMONSTRATION OF SYMMETRY, INSTABILITY, AND TRANSITION IN
FLUID MECHANICAL SYSTEMS.**

We have two Taylor-Couette cells. These have different sizes, so the range of Taylor number can be quite large. The Taylor cell is a fixed cylinder with a rotating (solid) inner cylinder. The gap is filled with silicone oil laced with aluminum flakes for visualization. Inner rotation stresses the fluid. The V(r) distribution so formed is subject to various centrifugal and secondary shear flow instabilities.

Taylor number Ta = 4 Omega^2 D^4 / *v*^2, where Omega is the
rotation period of the inner cylinder, D is the gap width, and *v *is the
viscosity (~ 1.5 cs for the silicone oils used).

To operate:

- Turn the motor on high to create turbulence and stir up the aluminum flake suspension for visualization
- Return to rest state
- Slowly increase rotation rate, leading to axisymmetric instability, secondary instability and turbulence
- Can use two separate apparati to demonstrate (approximate) self-similarity [where two systems of different physical size should behave similarly if the non-dimensional numbers, here Ta, are the same]
- Use to illustrate symmetry and symmetry breaking (axial, azimuthal, time, etc.)

Large apparatus with speed control (lower right). Attach belt (not shown) to various pulleys to create wide range of rotation rates.

Axisymmetric Taylor Vortices (the first symmetry breaking instability)

Turbulent flow. Note the remnants of large scale structure associated with the original Tayor Vortices in spite of the fact that the motion is highly turbulent.