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

Using data from direct numerical simulations in the Reynolds number range 8≤^Rλ≤1000, where ^Rλ 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 0.91ρu′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 0.17Rλ13 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.