Growth Rate of Kolmogorov Flow

This Demonstration shows the growth rate of Kolmogorov flow: there are two curves in the plot for different dimensions of the linear system. The fact that the two lines are indistinguishable (for large enough ) suggests that our choice of dimension is large enough. For small , there is a difference between the two curves, and we need to increase .

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DETAILS

This Demonstration is based on [1], which carries out a linear stability analysis of (incompressible) Kolmogorov flow.
Following the conventions in that paper, the forcing wavenumber is unity and the forcing amplitude is . The steady state velocity amplitude is therefore , where is the viscosity. By assuming the amplitude is unity, we have .
Reference
[1] L. Meshalkin, and Ya. G. Sinai, "Investigation of the Stability of a Stationary Solution of a System of Equations for the Plane Movement of an Incompressible Viscous Fluid," J. Appl. Math. Mech. 25, 1961 pp. 1700–1705.
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