Cascades of energy and helicity in axisymmetric turbulence

Abstract

A spectral analysis of strictly axisymmetric turbulence is performed. Both freely decaying and statistically steady flows are considered. In helical flows we identify a dual cascade, where energy is transferred towards the large scales and helicity to the smallest ones. It is shown that even in the absence of net helicity, a dual cascade persists, transferring energy backward and positively and negatively polarized helicity fluctuations forward.

Transition from non-swirling to swirling axisymmetric turbulence

“…For the definition of the energy spectra and the spectral fluxes we refer to Ref. [9]. When c T /c P < 1 [Fig.…”

“…5 and 6 we document all terms on the right-hand side of Eqs. (9) and (10). Insight in the behavior of these terms will allow us to model and thereby better understand the dynamics of the system.…”

“…The forcing band, 11 k 15, corresponds to scales intermediate in size between the dissipation scale and the cylinder size, as in Ref. [9], which allows for the existence of cascades towards both small and large scales. The forcing coefficients were set such that c r = c z ≡ c P and c θ ≡ c T .…”

“…This system is intermediate between 2D and 3D turbulence and was recently investigated by direct numerical simulation. It was shown in particular that an inverse energy cascade, responsible for the generation of large-scale coherent structures, and a direct helicity cascade towards small scales can coexist in this flow [8,9]. As predicted from theoretical works using statistical mechanics tools [10][11][12], different turbulent states were obtained for non-swirling (zero azimuthal velocity component, 2D2C) and for swirling flows (2D3C).…”

“…Contrary to the configuration investigated in Refs. [8,9], in which the flow was periodic in the axial direction, we imposed a confinement of the fluid in the cylindrical domain by using a suitable choice of the axial mode numbers n [17]. We carried out 150 simulations in a cylindrical domain of radius R = π and height H = 1.7π .…”