Energetics and vortex structures near small-scale shear layers in turbulence

Abstract

Vortices and kinetic energy distributions around small-scale shear layers are investigated with direct numerical simulations of isotropic turbulence. The shear layers are examined with the triple decomposition of a velocity gradient tensor. The shear layers subject to a biaxial strain appear near vortices with rotation, which induce energetic flow that contributes to the shear. A similar configuration of rotating motions near the shear layers is observed in a multi-scale random velocity field, which is free from the dynamics of turbulence. Therefore, the mechanism that sustains shearing motion is embedded as a kinematic nature in random velocity fields. However, the biaxial strain is absent near the shear layers in random velocity because rotating motions appear right next to the shear layers. When a random velocity field begins to evolve following the Navier–Stokes equations, the shear layers are immediately tilted to the nearby rotating motions. This misalignment is a key for the vortex to generate the compressive strain of the biaxial strain around the shear layer. As the configuration of shearing and rotating motions arises from the kinematic nature, the shear layers with the biaxial strain are formed within a few times the Kolmogorov timescale once the random velocity field begins to evolve. The analysis with high-pass filtered random velocity suggests that this shear layer evolution is caused by small-scale turbulent motions. These results indicate that the kinematic nature of shear and rotation in velocity fluctuations has a significant role in the formation of shear layers in turbulence.