Statistics and structures of pressure in isotropic turbulence

Abstract

Statistics and structures of pressure in three-dimensional incompressible isotropic turbulence are studied using high-resolution direct numerical simulation for Taylor microscale Reynolds numbers up to 220. It is found that the probability distribution function (PDF) of pressure has negative skewness due to both kinematic and dynamic effects, in contrast to the statistics of the pressure head, whose PDF is almost symmetric. The statistical relations among pressure, vorticity, dissipation and kinetic energy are investigated using conditional averaging. The averaged pressure, conditional on the local enstrophy, shows a linear dependence on enstrophy in the high-enstrophy region. Structure relations between pressure and other physical quantities are qualitatively examined using three-dimensional visualization of iso-surfaces. It is found that the high-vorticity regions are strongly correlated with the low-pressure regions. However, it appears that experimental visualization techniques for detecting high-intensity vortices using microbubbles in low-pressure regions might only be valid for those very-high-vorticity regions where the local enstrophy is at least five times higher than the root mean square enstrophy. The scaling law of the pressure structure function is also presented for both conventional and extended self-similarity. It is found that the pressure increment, δrp, scales with the velocity increment, δru, for the Reynolds numbers studied: δrp∼δru. For flows at moderate Reynolds numbers, it is demonstrated that the extended self-similarity gives better pressure scalings than results from traditional similarity solutions.