Characteristics of shearing motions in incompressible isotropic turbulence

Regions with shearing motions are investigated in isotropic turbulence with the triple decomposition, by which a velocity gradient tensor is decomposed into three components representing an irrotational straining motion, a rotating motion, and a shearing motion. A mean flow around the shearing motions shows that a thin shear layer is sustained by a biaxial strain, which is consistent with Burgers' vortex layer. The thickness of each shear layer is well predicted by Burgers' vortex layer. A comparison between genuine turbulence and a random velocity field confirms that the biaxial strain acting on the shear is a dynamical consequence from the Navier-Stokes equations rather than from a kinematic relation. The interplay between the shear and biaxial strain causes enstrophy production and strain self-amplification. For a wide range of Reynolds number, the shear is strong enough for the instability to cause a roll-up of the shear layer, where the perturbation grows much faster than large-scale turbulent motions.