Environmental Science and Engineering Seminar

Small-scale turbulence is a hallmark of countless natural and engineered flows. Its structural, statistical, and dynamical features are commonly understood in terms of velocity gradients. Conventionally, the velocity gradient tensor is decomposed into the symmetric strain-rate tensor, which describes the deformation rate of a fluid parcel, and the antisymmetric vorticity tensor, which describes its rotation rate. These tensors pervade analyses of turbulent flows, from identifying vortices to diagnosing energy transfer to modeling unresolved motions. But do they tell the whole story?

I will introduce a normality-based analysis of velocity gradients that sheds new light on the building blocks of turbulent flows. It refines the symmetry-based decomposition into strain and rotation by identifying a third contribution from shearing, a combination of strain and rotation distinguished by its non-normality. This approach captures the fingerprints of regimes and mechanisms in turbulent flows that are obscured by the symmetry-based approach. Crucially, it reveals the essential—perhaps surprising—contribution of shear layers to the sustenance of turbulence. The insights gleaned by this approach have direct implications for the design and evaluation of turbulence models. Although derived from prototypical numerical simulations, they also have the potential to enhance our ability to understand and model turbulence in environmental settings.