Revisiting Taylor's Hypothesis in Homogeneous Turbulent Shear Flow

Taylor’s Hypothesis of frozen flow has frequently been used to convert temporal experimental measurements into a spatial domain and its validity is of

crucial importance for experimental studies and theoretical investigations. Results from direct numerical simulations are used here to study the

applicability of Taylor’s Hypothesis in homogeneous turbulent shear flow by considering the correlation of the Eulerian acceleration with the convective

acceleration (i.e., the nonlinear term). Using a wavelet-based scale decomposition of the accelerations, their correlations at different scales of motion

are investigated. This approach allows us to revisit Taylor's Hypothesis by examining the cancellation properties of Eulerian and convective accelerations

at different flow scales. The results show that Taylor's hypothesis holds at small scales of the flow as reflected by the anti-alignment of the Eulerian

acceleration and the convective term. Such anti-alignment, however, is not observed at the largest scales of the turbulent motion, indicating that

Taylor's hypothesis does not generally hold for homogeneous turbulent shear flow.