Some results on the Reynolds number scaling of pressure statistics in isotropic turbulence

Abstract

Using data from direct numerical simulations in the Reynolds number range 8 ≤ R λ ≤ 1000 , where R λ is the Taylor microscale Reynolds number, we assess the Reynolds number scaling of the microscale and the integral length scale of pressure fluctuations in homogeneous and isotropic turbulence. The root-mean-square (rms) pressure (in kinematic units) is about 0.91 ρ u ′ 2 , where u ′ is the rms velocity in any one direction. The ratio of the pressure microscale to the (longitudinal) velocity Taylor microscale is a constant of about 0.74 for very low Reynolds numbers but increases approximately as 0.17 R λ 1 / 3 at high Reynolds numbers. We discuss these results in the context of the existing theory and provide plausible explanations, based on intermittency, for their observed trends.