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The stability of two-dimensional linear flows. (English) Zbl 0585.76045
(From authors’ summary.) A theoretical investigation is made of the linear stability of a viscous incompressible fluid undergoing a steady, unbounded two-dimensional flow in which the velocity field is a linear function of position. Such flows can be characterized completely by a single parameter \(\lambda\) which ranges from \(\lambda =0\) for simple shear flow to \(\lambda =1\) for pure extensional flow. The linearized velocity disturbance equations are analyzed for an arbitrary spatially periodic initial disturbance to give the asymptotic behavior of the disturbance at large time for \(0\leq \lambda \leq 1\). In addition, a complete analytical solution of the vorticity disturbance equation is obtained for the case \(\lambda =1\). It is found that unbounded flows with \(0<\lambda \leq 1\) are unconditionally unstable and an instability criterion is obtained.
Reviewer: M.Boudourides

MSC:
76E05 Parallel shear flows in hydrodynamic stability
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