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We explore the direct modification of the pseudo-spectral truncation of 2D,incompressible fluid dynamics to maintain a prescribed kinetic energy spectrum.The method provides a means of simulating fluid states with defined spectralproperties, for the purpose of matching simulation statistics to giveninformation, arising from observations, theoretical prediction or high fidelitysimulation. In the scheme outlined here, Nos\'e-Hoover thermostats, commonlyused in molecular dynamics, are introduced as feedback controls applied toenergy shells of the Fourier-discretized Navier-Stokes equations. As wedemonstrate in numerical experiments, the dynamical properties (quantifiedusing autocorrelation functions) are only modestly perturbed by our device,while ensemble dispersion is significantly enhanced in comparison withsimulations of a corresponding truncation incorporating hyperviscosity.

Direct control of the small-scale energy balance in 2D fluid dynamics