Effect of pressure on joint cascade of kinetic energy and helicity in compressible helical turbulence.

Abstract

Direct numerical simulations of three-dimensional compressible helical turbulence are carried out at a grid resolution of 1024^{3} to investigate the effect of pressure, which is important for the joint cascade of kinetic energy and helicity in compressible helical turbulence. The principal finding is that the pressure term of the helicity equation [defined as Φ^{H}=p∂_{i}(ω_{i}/ρ)] has a smaller effect on the helicity cascade in the aspect of amplitude and a smaller effective range, which leads to a longer inertial subrange of the helicity cascade, in contrast to a kinetic energy cascade. In addition, we also find that the effective range of Φ^{H} is concentrated only in large scales statistically, which is similar to the effect of the pressure term of the kinetic energy equation (defined as Φ^{E}=p∂_{i}u_{i}). From the overall sense of the effect of Φ^{E} and Φ^{H} on the kinetic energy and the helicity, respectively, both of them play a role of dissipation especially in the compression region. We propose that high enough helicity can affect the process of energy transformation between kinetic energy and internal energy, which means that the absolute local helicity hinders the process of kinetic energy transferring to internal energy, and promotes internal energy transferring to kinetic energy. In addition, Φ^{H} plays a source role both for positive and negative helicity. We also study the mechanism of cancellations between compression and rarefaction regions, and we find that the impact of a shocklet on the helicity cascade can be ignored statistically.