César Dopazo | Searcharxiv

arXiv2025

Scalar probability density function mixing models need not comply with the linearity and independence hypothesis

In a mixture of scalar fields undergoing diffusive processes governed by Fick's law, the concentration at each point evolves linearly in the concentrations at all points and independently from the other concentrations, when one considers a finite differences integration of their evolution equations. However, these properties must not necessarily be enforced in probability density function models, since they are relaxed when conditional expected values are taken.

physics.flu-dyn↗

arXiv2025

Fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic turbulence

A compact expression of fourth-order statistical moments of the velocity gradient tensor in homogeneous, isotropic, incompressible turbulence is obtained as a function of its invariants and of generic components of the velocity gradient. This single, compact expression is in full agreement with the four different expressions previously obtained by Siggia as functions of the same invariants and of generic components of the vorticity vector and the strain tensor; however, some discrepancies arise with respect to a similar, single expression obtained by Phan-Thien and Antonia. The used algorithm may be easily extended to handle higher order statistical moments of the velocity gradient.

physics.flu-dyn↗