Scale-Dependent Geometric Statistics of Homogeneous Turbulent Shear Flow

Scale-dependent geometrical statistics are introduced in order to consider the alignment properties of different vector-valued flow quantities. The vector fields are developed into an orthogonal wavelet series and the angle of the scale-wise contributions of different vector quantities, which are mutually orthogonal, can thus be quantified. This allows us to revisit Taylor's random hypothesis by examining the cancellation properties of Eulerian and convective accelerations at different flow scales, which is motivated by the authors' recent work in Phys. Rev. Fluids, 6, 074609, 2021. The obtained results for homogeneous turbulent shear flow, computed by direct numerical simulation, support that Taylor's hypothesis holds at small scales of the flow, reflected by the anti-alignment of the Eulerian acceleration and the convective term.