Title: A Schur decomposition reveals the richness of structure in homogeneous, isotropic turbulence as a consequence of localised shear,
Abstract: An improved understanding of turbulence is essential for the effective
modelling and control of industrial and geophysical processes. Homogeneous,
isotropic turbulence (HIT) is the archetypal field for developing turbulence
physics theory. Based on the Schur transform, we introduce an additive
decomposition of the velocity gradient tensor into a normal part (containing
the eigenvalues) and a non-normal or shear-related tensor. We re-interrogate
some key properties of HIT and show that the the tendency of the flow to form
disc-like structures is not a property of the normal tensor; it emerges from an
interaction with the non-normality. Also, the alignment between the vorticity
vector and the second eigenvector of the strain tensor is another consequence
of local shear processes.