Effects of helicity on dissipation in homogeneous box turbulence

Abstract

The dimensionless dissipation coefficient β = εL/U 3 , where ε is the dissipation rate, U the root-mean-square velocity and L the characteristic scale of the largest flow structures, is an important characteristic of statistically stationary homogeneous turbulence. In studies of β, 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 β on H f and find that it decreases β 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 β 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.

Dual channels of helicity cascade in turbulent flows

“…Under the influence of the second channel of helicity cascade, the small scales do not easily receive energy from large scales, and viscosity is not inclined to work well in near-dissipation regions. This conclusion is consistent with previous opinions that helicity can decrease the viscous dissipation of energy (Linkmann 2018).…”

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

“…In fully developed turbulent flows, it is shown in Ishihara et al () and Djenidi et al () that the effective amount of kinetic energy dissipation, measured in terms of its dimensional evaluation , tends to a constant close to 1/2 for a variety of laboratory and numerical experiments, in the forced case as well as for decaying flows provided their Taylor Reynolds numbers be sufficiently high, but there is also a marked deficiency, of the order of 10%, in the presence of nonzero helicity (Linkmann, ). The actual amount of dissipation (as opposed to that expected for a field composed of a superposition of linear waves interacting weakly) directly influences the overall atmospheric and oceanic energetic exchanges, and it can also modify conditions for acoustic transmission, as well as for deepwater drilling.…”

Linearly forced isotropic turbulence at low Reynolds numbers

“…The constant C in this nonlinear contribution sets the asymptotic value of the normalized dissipation rate L/K 3/2 [11] and represents thereby the dissipative anomaly [12], i.e., a nonvanishing dissipation when the viscosity tends to zero. It is indeed observed that L/K 3/2 tends to a constant at high Reynolds numbers for a given flow [13], but its value can depend on the large-scale structure of the energetic scales [14], the presence of helicity [15], or the instationarity (as observed in Ref. [16] and explained in Ref.…”

“…[17]). Model 1 was rigorously derived as an upperbound for turbulent dissipation in the Navier-Stokes equations both for static forcing [18,19] and dynamic forcing [15]. The low Reynolds limit of Model 1 was shown to quite accurately describe the results of simulations and closure in references [10,14].…”