Evidence of an asymptotic geometric structure to the Reynolds stress motions in turbulent boundary layers

Recent results suggest that the $uv$ motions in turbulent wall-flows asymptotically exhibit self-similar geometric properties. Herein we use time series from high resolution boundary layer experiments up to high Reynolds numbers to discern additional properties associated with the $uv$ signals. Their space filling properties are shown to reinforce previous observations, while the $uv$ skewness profile suggests that the size and magnitude of these motions are correlated on the inertial domain. The size and length scales of the negative $uv$-motions are shown to increase with distance from the wall, while their occurrences decreases. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to $\langle -uv \rangle$ are distinctly larger than their average size. The $u$ and $v$ cospectra, however, exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, $W(y)$, of the scaling layer hierarchy surmised from analysis of the mean momentum equation. This distribution is associated with scale dependent zero-crossings in the contributions to $\langle -uv \rangle$, and derivative cospectra of $\langle -uv \rangle$ support the existence of this structural detail.