Enstrophy transfers in helical turbulence

In this paper we study the enstrophy transfers in helical turbulence using direct numerical simulation. We observe that the helicity injection does not have significant effects on the inertial-range energy and helicity spectra ($\sim k^{-5/3}$) and fluxes (constants). We also calculate the separate contributions to enstrophy transfers via velocity-to-vorticity and vorticity-to-vorticity channels. There are four different enstrophy fluxes associated with the former channel or vorticity stretching, and one flux associated with the latter channel or vorticity advection. In the inertial range, the fluxes due to vorticity stretching are larger than that due to advection. These transfers too are insensitive to helicity injection.

Figure 1

Illustration of the five enstrophy fluxes in addition to the kinetic energy flux ${\mathrm{\Pi }}_{u<}^{u>}\equiv {\mathrm{\Pi }}_E$ which is defined in Eq. (39).

Figure 2

Time evolution of (a) energy dissipation, (b) helicity dissipation, and (c) enstrophy dissipation for the same energy injection rate ${\epsilon }_E=0.1$ and three different helicity injections ${\epsilon }_H=0,0.1,0.2$. For $t\ge 10$ a steady state is reached with a mean enstrophy dissipation about 160.9.

Figure 3

Normalized energy spectra (solid curves) and helicity spectra (dashed curves) with the same color code as in Fig. 2. In the inset, normalized energy fluxes (solid curves) and helicity fluxes (dashed curves). The black dashed curves correspond to the analytical formulas (40, 41, 42, 43).

Figure 4

The five enstrophy fluxes given in Eqs. (17, 18, 19, 20, 21) and the sum ${\mathrm{\Pi }}_{\omega >}^{u<}+{\mathrm{\Pi }}_{\omega <}^{u>}+{\mathrm{\Pi }}_{\omega <}^{u<}+{\mathrm{\Pi }}_{\omega >}^{u>}$ are plotted for ${\epsilon }_E=0.1$ and ${\epsilon }_H=0$.