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≤10008≤Rλ≤1000, where RλRλ 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′20.91ρu′2, where u′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 0.17Rλ1/3 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.

► Direct numerical simulations at Taylor Reynolds numbers RλRλ up to 1000 are used to study the scaling of pressure fluctuations and length scales.
► Root-mean-square (rms) pressure scales with rms velocity and is independent of the Reynolds number.
► The ratio of pressure microscale to velocity Taylor microscale is constant at low Reynolds numbers but increases as Rλ1/3 for high RλRλ.
► The ratio of pressure and velocity integral length scales is independent of the Reynolds number.
► Results are inconsistent with classical phenomenology; introduction of intermittency corrections may explain the observed trends.