The response of small-scale shear layers to perturbations in turbulence

Abstract

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$ . Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$ . Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

Efficient enhancement of turbulent entrainment by small-scale shear instability

“…2020 b ). Recent studies of small-scale shear layers confirmed the optimal wavelength for the small-scale shear instability, which is approximately 30 times the Kolmogorov scale (Watanabe & Nagata 2023). When turbulence is subject to perturbations of this wavelength, the shear layers promptly collapse, resulting in a higher population of vortices arising from the shear instability.…”

“…The perturbed velocity field is formulated as . A prior study addressed the impacts of on small-scale shear instability in HIT, where the changes due to the promoted instability were discussed in terms of the number of vortices, energy dissipation, enstrophy production and strain self-amplification (Watanabe & Nagata 2023). Adopting this same methodology, is described using sinusoidal functions: , where is the amplitude, and is the wavelength.…”

“…Adopting this same methodology, is described using sinusoidal functions: , where is the amplitude, and is the wavelength. Different perturbation forms, such as random disturbances with a single length scale, were tested for HIT (Watanabe & Nagata 2023), showing that the evolution of perturbed HIT remains independent of perturbation type.…”

“…Cases incorporating perturbations are designated as R with , indicating the Reynolds number, where or L distinguishes the wavelength , and is the normalised amplitude. The designation corresponds to a perturbation of , namely the optimal wavelength of small-scale shear instability (Watanabe & Nagata 2023), whereas assumes a larger wavelength, . The normalised amplitude ranges between 1.0 and 2.6.…”

“…The evolution of shear layers is largely unaffected by perturbations with wavelengths much larger or smaller than . The optimal perturbation wavelength was determined using two simulations (Watanabe & Nagata 2023). One is a direct numerical simulation (DNS) of turbulent flows, which examines the length and velocity scales of the shear layers.…”