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Abstract A new mixed scaling parameterZ=z/(Lh)^1/2is proposed for similarity in the stable atmospheric surface layer, wherezis the height,Lis the Obukhov length, andhis the boundary layer depth. In comparison with the parameterζ=z/Lfrom Monin–Obukhov similarity theory (MOST), the new parameterZleads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on bothZandζ. The proposed mixed scaling ofZand relevance ofhcan be explained by physical arguments related to the limit ofz-less stratification that is reached asymptotically above the surface layer. The presented evidence and fitted similarity relations are promising, but the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here. 

Abstract A persistent spatial organization of eddies is identified in the lowest portion of the stably stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al. in J Atmos Sci 73(4):1815–1840, 2016) ranging in stability from near-neutral to almost z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for near-neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in eddy size with increasing stratification, which is empirically captured by existing Monin–Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions. 

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions – both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of ‘wrinkles’ along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power-law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power-law exponent for the structure function can be recovered by considering the collective behaviour of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces. 

The statistical properties of prograde spanwise vortex cores and internal shear layers (ISLs) are evaluated for a series of high-Reynolds-number turbulent boundary layers. The considered flows span a wide range of both Reynolds number and surface roughness. In each case, the largest spanwise vortex cores in the outer layer of the boundary layer have size comparable to the Taylor microscale $$\lambda _T$$ , and the azimuthal velocity of these large vortex cores is governed by the friction velocity $${u_\tau }$$ . The same scaling parameters describe the average thickness and velocity difference across the ISLs. The results demonstrate the importance of the local large-eddy turnover time in determining the strain rate confining the size of the vortex cores and shear layers. The relevance of the turnover time, and more generally the Taylor microscale, can be explained by a stretching mechanism involving the mutual interaction of coherent velocity structures such as uniform momentum zones with the evolving shear layers separating the structures.