Statistics of Pressure Fluctuations in Decaying, Isotropic Turbulence

TL;DR

This study uses direct numerical simulations to analyze pressure fluctuations in decaying isotropic turbulence, revealing detailed statistical properties, structures, and orientations of pressure-related tensors and their evolution.

Contribution

It provides new insights into the statistical and structural properties of pressure fluctuations and tensors in decaying isotropic turbulence, including the first analysis of the non-local pressure-hessian tensor.

Findings

Isosurfaces of low pressure form slender filaments and sheet-like structures.

Probability distributions of pressure differences and gradients are characterized.

Statistical orientations between pressure and flow tensors are identified.

Abstract

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.