Inproceedings,
The Stability of Two-Dimensional Linear Flow
Eighth Australasian Fluid Mechanics Conference, (1983)
Abstract
The paper reports a theoretical investigation of the stability of a viscous incompressible fluid undergoing two-dimensional flow in which the velocity field is a linear function of position. Such flows are approximately generated by the four-roll mill device of G. I. Taylor and are described by a parameter \$łambda\$ ranging from \$łambda=0\$ for simple shear flow to \$łambda=1\$ for pure extensional flow. An instability criterion relating the initial disturbance wave vector \$\vec\alpha\$ to the steady flow strain rate \$E\$, kinematic viscosity \$\nu\$ and the parameter \$łambda\$ is obtained showing that for all admissible values of \$E\$ and \$\nu\$, a wave vector \$\vec\alpha\$ may be found which corresponds to disturbances which grow exponentially in time.
