Effects of helicity on dissipation in homogeneous box turbulence

Abstract

The dimensionless dissipation coefficient $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D700}L/U^{3}$, where $\unicode[STIX]{x1D700}$ is the dissipation rate, $U$ the root-mean-square velocity and $L$ the integral length scale, is an important characteristic of statistically stationary homogeneous turbulence. In studies of $\unicode[STIX]{x1D6FD}$, the external force is typically isotropic and large scale, and its helicity $H_{f}$ either zero or not measured. Here, we study the dependence of $\unicode[STIX]{x1D6FD}$ on $H_{f}$ and find that it decreases $\unicode[STIX]{x1D6FD}$ by up to 10 % for both isotropic forces and shear flows. The numerical finding is supported by static and dynamical upper bound theory. Both show a relative reduction similar to the numerical results. That is, the qualitative and quantitative dependence of $\unicode[STIX]{x1D6FD}$ on the helicity of the force is well captured by upper bound theory. Consequences for the value of the Kolmogorov constant and theoretical aspects of turbulence control and modelling are discussed in connection with the properties of the external force. In particular, the eddy viscosity in large-eddy simulations of homogeneous turbulence should be decreased by at least 10 % in the case of strongly helical forcing.