A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence

Pressure fluctuations in incompressible turbulence are studied by direct numerical simulations of the three-dimensional (3-D) Navier–Stokes equations. The pressure probability distribution function (PDF) is shown to have an exponential tail on the negative side, and to be independent of the Reynolds number for Reλ≲60. At higher Reynolds numbers, the low pressure part of the pressure PDF becomes super exponential. The joint PDFs of strain, vorticity, and pressure (considered pairwise) show a strong dissymmetry between positive and negative pressure fluctuations. The results obtained from the numerical solutions of the Navier–Stokes equations are compared with a Gaussian velocity field. The two statistical ensembles are shown to lead to quantitatively different results.