Resolvent analysis of the two-dimensional Kolmogorov flow

We use the resolvent analysis framework to study the two-dimensional (2-D) Kolmogorov flow, i.e. the 2-D Navier Stokes equations forced by a sinusoidal body force. In the resolvent analysis, the non-linear terms of the Navier-Stokes equations are considered to be an unknown forcing to the linear equations. The aim here is to construct a reduced-order model of the 2-D Kolmogorov flow. We therefore ask the question of what the best basis in the temporal direction is, a Fourier basis or a Wavelet basis, that would give the optimum reduced-order model of the flow?

The authors would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the program 'Mathematical Aspects of Turbulence: Where do we stand?' where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1.