Joint multifractal analysis of intermittent fields in high-resolution DNS of turbulence

In high-Reynolds number turbulence, several intermittent fields coexist, among which are the rate \textit{$\varepsilon $} of dissipation of turbulent energy, vorticity \textit{$\omega $} and pressure gradients grad$p$, etc. These intermittent fields display different degrees of correlation among them. To characterize such coexisting distributions of intermittent fields in high-Reynolds number turbulence, we apply joint multifractal analysis to the data obtained by high-resolution DNS of turbulence in a periodic box. The analysis shows that the degree of correlation between \textit{$\alpha $}$_{\varepsilon }$ and \textit{$\alpha $}$_{P}$ is considerably high, but lower than between \textit{$\alpha $}$_{\varepsilon }$ and \textit{$\alpha $}$_{\Omega }$, where $P=\vert $grad$p\vert ^{2}$ and \textit{$\Omega $ }=\textit{$\omega $}$^{2}$/2, and \textit{$\alpha $}$_{{\rm A}}$ is a local singularity strength of $A$.