On the scale-dependent turbulent convection velocity in a spatially developing flat plate turbulent boundary layer at Reynolds number

Abstract

The scale-dependent turbulent convection velocity of streamwise velocity fluctuations resolved by large eddy simulation is investigated for the first time across the whole profile of a zero-pressure-gradient spatially developing smooth flat plate boundary layer at $\mathit{Re}_{{\it\theta}}=13\,000$. The high Reynolds number and streamwise heterogeneity constraints motivate the derivation of a dedicated new method to assess the frequency-dependent convection velocity from time signals and their local streamwise derivative, using estimates of power spectral densities (PSDs). This method is inspired by del Álamo & Jiménez (J. Fluid Mech., vol. 640, 2009, pp. 5–26), who treated a lower Reynolds number channel flow with a method suited to spectral direct numerical simulations of streamwise homogeneous flows. Reconstruction of the streamwise spectrum from the time spectrum using the scale-dependent convection velocity is illustrated and compared with classical strategies. The new method inherently includes not only the assessment of the validity of Taylor’s hypothesis, whose trend is remarkably consistent with theoretical predictions by Lin (Q. Appl. Maths, vol. X(4), 1953, 154–165), but also the definition of a global convection velocity accounting for any arbitrary frequency band. This global velocity is shown to coincide with a correlation-based method widely used in experiments. In addition to the mathematical least-squares definition of this velocity, new interpretations based on the flow physics and turbulent micro time scales are presented. Further, the group velocity is assessed and its relation to convection is discussed.