Pressure spectrum and structure function in homogeneous turbulence

The pressure spectrum and structure function in homogeneous steady turbulence of an incompressible fluid is studied using direct numerical simulation. The resolution of the simulation is up to $1024^3$ and the Taylor microscale Reynolds number $\Rl$ is between 38 and 478. The energy spectrum is found to have a small but finite inertial range followed by a bump at large wavenumbers. The Kolmogorov constant $K$ is found to be $1.66\pm 0.08$. The pressure spectrum also has a small but finite inertial range of $P(k)=B_p\eb^{4/3}k^{-7/3}$ followed by a bump of nearly $k^{-5/3}$ range at higher wavenumbers. Both scaling ranges match at a crossover wavenumber, $k_p$, which is a characteristic wavenumber for the pressure gradient. The constant $B_p$ is found to be about $8.34\pm 0.15$ for $\Rl=460$. Its non-universality is discussed. The second order pressure structure function, computed in terms of the fourth order velocity structure functions, agrees well with that obtained by the direct measurement over separations ranging between the inertial and dissipation scales.