Couette flow

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The term Couette flow refers to the laminar flow of a viscous liquid in the space between two surfaces, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid. This type of flow is named in honor of Maurice Frédéric Alfred Couette, a Professor of Physics at the French university of Angers in the late 19th century.

Most commonly, the term "Couette flow" refers to the flow between two planes moving relative to one another (but with constant separation between the two planes). Other examples include the flow between two concentric spheres with a common axis of rotation, or the flow between two coaxial cylinders with one of the cylinders rotating at some angular velocity relative to the other. This latter type of flow is usually referred to as Taylor-Couette flow, which honors the work of G. I. Taylor on the theoretical hydrodynamic stability of this flow.

Linear Couette flow is not subject to any linear instabilities. Experiments on linear Couette flow are difficult to perform for obvious reasons having to do with boundary conditions; however, experimental and numerical evidence strongly suggests that linear Couette flow is unstable to breakdown to turbulence despite the lack of any linear instabilities. A similar problem occurs in the case of various types of Poiseuille flow, such as flow through a perfect cylindrical pipe.

In the case of Taylor-Couette flow, i.e. Couette flow between cylinders, the flow is subject to linear instabilities, for certain values of the rotation speeds of the inner and outer cylinders. See, e.g. the article on Taylor vortices. However, again it should be noted that it appears that it is possible to induce a turbulent state even for rotation speeds for the inner and outer cylinders for which there is no known linear instability. For a given ratio of outer cylinder rotation speed to inner cylinder rotation speed, and for a given ratio of outer cylinder radius to inner cylinder radius, the system is unstable once the Taylor number (a quantity that characterizes the importance of rotation of a fluid about a vertical axis) exceeds a critical value.