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.