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Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields

Title data

Wilczek, Michael ; Meneveau, Charles:
Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields.
In: Journal of Fluid Mechanics. Vol. 756 (2014) . - pp. 191-225.
ISSN 0022-1120
DOI: https://doi.org/10.1017/jfm.2014.367

Abstract in another language

Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon.

Further data

Item Type: Article in a journal
Refereed: Yes
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Physics > Chair Theoretical Physics I > Chair Theoretical Physics I - Univ.-Prof. Dr. Michael Wilczek
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 530 Physics
Date Deposited: 23 Feb 2022 13:40
Last Modified: 23 Feb 2022 13:40
URI: https://eref.uni-bayreuth.de/id/eprint/67590