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, Nos\'{e}-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.

Additional Metadata
Keywords atmospheric flows, computational methods, homogeneous turbulence
THEME Energy (theme 4)
Publisher Cambridge U.P.
Persistent URL dx.doi.org/10.1017/jfm.2015.526
Journal Journal of Fluid Mechanics
Project Thermostat closures for inviscid fluids
Citation
Frank, J.E, Leimkuhler, B.J, & Myerscough, K.W. (2015). Direct control of the small-scale energy balance in two-dimensional fluid dynamics. Journal of Fluid Mechanics, 782, 240–259. doi:10.1017/jfm.2015.526