Dynamics of vortical structures in a homogeneous shear flow

Abstract

The mechanism of generation, development and interaction of vortical structures, extracted as concentrated-vorticity regions, in homogeneous shear turbulence is investigated by the use of the results of a direct numerical simulation of the Navier-Stokes equation with 1283 grid points. Among others, a few of typical vortical structures are identified as important dynamical elements, namely longitudinal and lateral vortex tubes and vortex layers. They interact strongly with each other. Longitudinal vortex tubes are generated from a random fluctuating vorticity field through stretching of fluid elements caused by the mean linear shear. They are inclined toward the streamwise direction by rotational motion due to the mean shear. There is a small (about 10°) deviation in direction between the longitudinal vortex tubes and vorticity vectors therein, which makes the vorticity vectors turn toward the spanwise direction (against the mean vorticity) until the spanwise components of the fluctuating vorticity become comparable in magnitude with the mean vorticity. These longitudinal vortex tubes induce straining flows perpendicular to themselves which generate vortex layers with spanwise vorticity in planes spanned by the tubes and the spanwise axis. These vortex layers are unstable, and roll up into lateral vortex tubes with concentrated spanwise vorticity through the Kelvin-Helmholtz instability. All of these vortical structures, through strong mutual interactions, break down into a complicated smallscale random vorticity field. Throughout the simulated period an oblique stripe structure dominates the whole flow field: initially it is inclined at about 45° to the downstream and, as the flow develops, the inclination angle decreases but eventually stays at around 10°–20°.

Scaling laws and intermittency in homogeneous shear flow

“…The regeneration cycle just analyzed here for the statistical steady state phase is very similar to that described by Kida & Tanaka [10] for the early stages of evolution of the flow from isotropic initial conditions, suggesting that the operating mechanisms are substantially identical.…”

“…[9] discussed streamwise vortices and high and low speed streaks commenting on the similarities with the buffer region of wall bounded flows. In a more recent work Kida & Tanaka [10] proposed a regeneration mechanism for the streamwise vortices and pointed out the role of vortex sheet instability in the formation of new vortices. The present analysis deals with the same issues, but it is focused on the statistical steady state regime of the flow.…”

“…[9] studied the topology and mutual interactions of vorticity showing that many dynamical features are quite similar to those observed in the wall region of a turbulent boundary layer. A more detailed study on the same subject has been performed by Kida and Tanaka [10] who discussed the regeneration cycle of the streamwise vortices in a homogeneous shear flow.…”

Coherent structures in statistically stationary homogeneous shear turbulence

“…The simplest shear flow is unbounded homogeneous shear turbulence (HST), which, unfortunately, does not have an asymptotic statistically stationary state. Ideal HST in unbounded domains grows indefinitely, both in intensity and in length scale (Champagne, Harris & Corrsin 1970;Harris, Graham & Corrsin 1977;Lee et al 1990;Kida & Tanaka 1994), and simulations are typically discontinued as the growing length scale approaches the size of the computational box (Rogers & Moin 1987). However, Pumir (1996) extended the simulation to longer times and reached a statistically stationary state (SSHST) in which the largest-scale motion is constrained by the computational box and undergoes a succession of growth and decay phases of the kinetic energy and the enstrophy, reminiscent of the bursts in wall-bounded flows.…”

Coherent structures in statistically-stationary homogeneous shear turbulence

“…For example, Rogers & Moin (1987) showed typical 'hairpin' structures under shear rates comparable to those in the logarithmic layer of wall-bounded flows, and Lee et al (1990) found that higher shear rates, comparable to those in the buffer layer, result in structures similar to near-wall velocity streaks (Jimenez, 2013b). Those structures are known to play crucial roles in transition and in maintaining shear-induced turbulence (Jiménez & Moin, 1991;Jiménez, 1994;Hamilton et al, 1995;Waleffe, 1997), and Kida & Tanaka (1994a) proposed a generation mechanism for the streamwise vortices in transient HST that recalls those believed to be active in wall turbulence.…”