Abstract
In homogeneous turbulent flow, a relation for the correlation between velocity gradient and pressure Hessian was found recently: . We discuss the implications of this relation to the velocity gradient dynamics: together with the Poisson equation for pressure, the homogeneity relation yields an identity between and the integration of a two-point fourth-order correlation function of velocity gradient for isotropic flows. Our results indicate that the main contributions to come from scales less than roughly 20 times the Kolmogorov scale. Also, the homogeneity relation provides restrictions to the parameters in the closure models of pressure Hessian in velocity gradient dynamics. We further discuss the generalization of this homogeneity relation to turbulent shear flows, and we show numerically that this relation between and is approximately satisfied even in the presence of a shear and of a wall, as it occurs in turbulent channel flows.
- Received 25 October 2022
- Accepted 17 January 2023
DOI:https://doi.org/10.1103/PhysRevFluids.8.024601
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