Pressure Spectrum in Homogeneous Turbulence

The pressure spectrum in homogeneous steady turbulence is studied using direct numerical simulation with resolution up to ${1024}^3$ and the Reynolds number $R_{\lambda }$ between 38 and 478. The energy spectrum is found to have a finite inertial range with the Kolmogorov constant $K=1.65\mathrm{}\pm 0.05$ followed by a bump at large wave numbers. The pressure spectrum in the inertial range is found to be approximately $P\left(k\right){=B}_p{\overline{\epsilon }}^{4/3}{k}^{-7/3\mathrm{}}$ with $B_p=8.0\mathrm{}\pm 0.5$, and followed by a bump of nearly $k^{-5/3\mathrm{}}$ at higher wave numbers. Universality and a new scaling of the pressure spectrum are discussed.