On coherent-vortex identification in turbulence

TLDR

The study investigates coherent vortex identification using DNS and LES of turbulent flows. They use the Q criterion, based on the pressure Laplacian and the second invariant of the velocity gradient, to identify vortices in DNS/LES of various turbulent flows and compare it with classical methods, also applying conditional sampling to study quasi‑longitudinal vortices. The Q criterion reveals positive pressure Laplacian inside low‑pressure tubes, produces clear coherent vortices, isolates near‑wall vortical contributions to velocity and vorticity fluctuations, and elucidates the dynamics of Λ vortices in backward‑facing steps and transonic cavity flows.

Abstract

Abstract The identification issue of coherent vortices is investigated on the basis of direct numerical simulation (DNS) and large-eddy simulations (LES) of turbulent flows. It is first shown that the pressure Laplacian is positive within a low-pressure tube of small cross section enclosed by convex isobaric surfaces in a uniform-density flow. Since this quantity is related to the second invariant Q of ∇ u , the Q criterion (region where Q is positive) is a necessary condition for the existence of such tubes. This eduction scheme is compared to other classical methods in incompressible simulations of isotropic turbulence: a mixing layer, a channel flow and a backward-facing step. Q-isosurfaces turn out to display very nice coherent vortices. This criterion is also used in combination with a conditional sampling method to discuss the characteristics of quasi-longitudinal vortices in a manipulated channel flow. The contribution of near-wall vortical structures to velocity and vorticity fluctuations is clearly isolated. Finally, the Q criterion is applied to the eduction of Λ vortices in separated flows. The dynamics of these structures is discussed for an incompressible backward-facing step and a transonic flow past a rectangular cavity.