Growth Rate of Kolmogorov Flow

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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 .

Contributed by: Chi-kwan Chan (August 2012)
Open content licensed under CC BY-NC-SA


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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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