Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic, three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organised as slender filaments, whereas the predominant isostructures appear sheet-like. We exhibit several new results, including plots of probability distributions of the spatial pressure-difference, the pressure-gradient norm, and the eigenvalues of the pressure-hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-hessian tensor, the pressure-gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the non-local part of the pressure-hessian tensor are also exhibited, for the first time. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A {\bf 5}, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids {\bf 7}, 411 (1995)] concerning the pressure-hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.