Direct control of the small-scale energy balance in two-dimensional fluid dynamics

Jason Frank, Benedict Leimkuhler, Keith W. Myerscough

Research output: Contribution to journalArticlepeer-review

Abstract

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 spectral properties, for the purpose of matching simulation statistics to given information, arising from observations, theoretical prediction or high fidelity simulation. In the scheme outlined here, Nose-Hoover thermostats, commonly used in molecular dynamics, are introduced as feedback controls applied to energy shells of the Fourier-discretized Navier-Stokes equations. As we demonstrate in numerical experiments, the dynamical properties (quantified using autocorrelation functions) are only modestly perturbed by our device, while ensemble dispersion is significantly enhanced in comparison with simulations of a corresponding truncation incorporating hyperviscosity.
Original languageEnglish
Pages (from-to)240-259
JournalJournal of Fluid Mechanics
Volume782
Early online date7 Oct 2015
DOIs
Publication statusPublished - Nov 2015

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