Representation of the Reynolds stress tensor through quadrant analysis for a near-neutral atmospheric surface layer flow

Abstract

To disseminate the role of the eddy motions on the anisotropic states of the Reynolds stress tensor ($$\varvec{B}$$), we devise a novel methodology based on the quadrant analysis, where the distributions of the invariants of $$\varvec{B}$$ are studied on a $$u^{\prime }$$–$$w^{\prime }$$ quadrant plane, with $$u^{\prime }$$ and $$w^{\prime }$$ being the turbulent fluctuations in the streamwise and vertical velocities. We apply this methodology to a near-neutral atmospheric surface layer (ASL) flow, derived from a field experiment dataset having multi-level turbulence measurements. The results show that in a near-neutral ASL flow, the anisotropic states of $$\varvec{B}$$ are determined by the distribution of the streamwise and cross-stream velocity variances ($$\sigma _{u}^2$$ and $$\sigma _{v}^2$$) on the $$u^{\prime }$$–$$w^{\prime }$$ quadrant plane. By studying the contour maps of the invariants of $$\varvec{B}$$ on the $$u^{\prime }$$–$$w^{\prime }$$ quadrant plane, we discover three distinct zones with elliptical boundaries in the $$u^{\prime }$$–$$w^{\prime }$$ plane, across which the anisotropic states of the eddy motions evolve. We find that the eddy motions which occur We also notice that the distinction between these three zones in the $$u^{\prime }$$–$$w^{\prime }$$ plane is prominent at the lowest measurement level, but becomes progressively indistinguishable as the measurement height increases.