Enhanced and unenhanced dampings of Kolmogorov flow

In the present study, Kolmogorov flow represents the stationary sinusoidal solution (sin y, 0) to a two-dimensional spatially periodic Navier-Stokes system, driven by an external force. This system admits the additional nonstationary solution (sin y, 0)+e−νt(sin y, 0), which tends exponentially to the Kolmogorov flow at the minimum decay rate determined by the viscosity ν. Enhanced damping or enhanced dissipation of the problem is obtained by presenting higher decay rate for the difference between a solution and the non-stationary basic solution. Moreover, for the understanding of the metastability problem in an explicit manner, a variety of exact solutions are presented to show enhanced and unenhanced dampings.

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