Pressure Spectrum in Homogeneous Turbulence

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to 1024³ and the Reynolds number R_λ between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant K0ex0ex=0ex0ex1.65±0.05 followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately P(k)0ex0ex=0ex0exBₚε4/3k^-7/3 with Bₚ0ex0ex=0ex0ex8.0±0.5, and followed by a bump of nearly k^-5/3 at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.