Uniform momentum and temperature zones in unstably stratified turbulent flows

Abstract

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

Stochastic modelling of the instantaneous velocity profile in rough-wall turbulent boundary layers

“…The existence of UMZs in different flow conditions and configurations confirm their ubiquity and statistical relevance: for instance, in high-Mach-number flows (Williams et al 2018;Cogo et al 2022), above different wall surface roughness geometries or patterns (Xu, Zhong & Zhang 2019), in adverse pressure gradient TBL flows (Bross, Fuchs & Kähler 2019), in boundary layers perturbed by surface waves (Li et al 2020) and in the ASL under different thermal stability conditions (Puccioni et al 2023;Salesky 2023). The UMZs and the associated shear layers can be thus framed as the representative attached eddy, coherent structure responsible for the momentum transport and the establishment of the logarithmic velocity profile over a wide range of surface roughness conditions and Reynolds numbers (Prandtl 1925;Bautista et al 2019;Heisel et al 2020c).…”

“…2020) and in the ASL under different thermal stability conditions (Puccioni et al. 2023; Salesky 2023). The UMZs and the associated shear layers can be thus framed as the representative attached eddy, coherent structure responsible for the momentum transport and the establishment of the logarithmic velocity profile over a wide range of surface roughness conditions and Reynolds numbers (Prandtl 1925; Bautista et al.…”

Coherent structures in stably stratified wall-bounded turbulent flows

“…In § 4.2 we identified the existence of an outer peak in the premultiplied spectrograms in cases A-C, and in § 4.3 found enhanced linear coupling at the scales of these outer peaks. Previous studies of the CBL have shown that turbulent transports of momentum and scalars become increasingly dissimilar with increasing instability (Li & Bou-Zeid 2011;Dupont & Patton 2012;Patton et al 2016;Salesky 2023), andSalesky et al (2017) were able to connect this breakdown of Reynolds' analogy to varying modes of convective organization. However, the relationship between momentum and heat transport in stably 10 0 10 1 10 -1 10 0 10 1 10 -1 10 0 10 1 10 -1 10 0 10 1 stratified turbulent shear flows remains relatively unexplored.…”

The Chimera Revisited: Wall- and Magnetically-Bounded Turbulent Flows

“…The simultaneous existence of both UMZ and UTZ has been reported for both stably and unstably stratified turbulent flow by analysis of large eddy simulations (LESs) [65,66]. In [65], the stably stratified planetary boundary layer (PBL) was treated; it was found that UMZ and UTZ are "closely, but not perfectly related".…”

“…In [65], the stably stratified planetary boundary layer (PBL) was treated; it was found that UMZ and UTZ are "closely, but not perfectly related". Unstable stratified channel flow was covered in [66], where it was found that "Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. "…”