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

TL;DR

This paper introduces a novel method using Nosé-Hoover thermostats to directly control the energy spectrum in 2D fluid simulations, enabling precise spectral property matching while minimally affecting dynamics.

Contribution

It presents a new spectral control technique for 2D fluid dynamics using feedback thermostats, allowing targeted energy spectrum maintenance and improved ensemble dispersion.

Findings

Dynamical properties are only modestly affected by the control method.

Ensemble dispersion is significantly enhanced compared to hyperviscosity-based truncations.

The method enables simulation of fluid states with prescribed spectral characteristics.

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, 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.