The importance of non-normal contributions to velocity gradient tensor dynamics for spatially developing, inhomogeneous, turbulent flows

We investigate the properties of the velocity gradient tensor for spatially evolving turbulent flows (a near-wake, two axisymmetric jets and a planar mixing layer). Emphasis is placed on the study of the normal and non-normal parts of the tensor. Non-normality plays a greater role in the dynamics than is observed for HIT and does so for all spatial locations examined. This implies a greater role for viscosity or the deviatoric part of the pressure Hessian. Results for the wake flow, where we isolate the coherent part of the dynamics using a modal decomposition, clarifies how these competing

effects operate. Previous studies have shown the shape of the Q-R diagram (formed by the second and third invariants of the characteristic equation for the tensor) is approximately universal at small-scales for different flows. The non-normal dynamics are neglected in the Q-R approach but appear to differ significantly between flows.