Pattern Formation in Fluid Systems

Over a century ago, Maurice Couette created a simple device to measure the viscosity of a fluid. He placed the fluid between two concentric cylinders and measured the amount of torque required to turn the inner cylinder. As one increases the rotation rate of the inner cylinder, more torque is required. However, at a certain rotation rate, the variation of torque with cylinder speed changes abruptly. This occurs at the onset of an instability, the sudden change of the pattern of fluid flow as a parameter is varied. In this case, a series of circulating cells known as Couette-Taylor vortices emerge in the fluid flow . The presence of this instability places limits on the utility of Couette's viscometer. Many fluid instabilities have such practical consequences; for instance, the presence of fingering instabilities during oil extraction can mean that half of the oil in a reservoir is left in the ground. At the Center for Nonlinear Dynamics, we study fluid instabilities and pattern formation in many fluid systems.