Turbulence kinetic energy budget in the stable boundary layer over a heterogeneous surface

Abstract

This study presents turbulence kinetic energy (TKE) budget terms above tall, deciduous walnut canopy in the wintertime stable boundary layer (SBL) and makes a comparison to well‐known results of horizontally homogeneous and flat (HHF) terrain. Turbulence measurements performed at five levels above the canopy height (approximately h=18 m) enable the investigation of joint effect of the roughness sublayer (RSL) and the transition layer on the TKE budget terms. Each term of the TKE budget is investigated within the framework of local similarity theory. Kolomogorov's similarity hypothesis assumes local isotropy within the inertial subrange. Thoroughly testing the local isotropy hypothesis for the present dataset results in a ratio of the horizontal spectral densities (Sv/Su) approaching 4/3, while the ratio of the vertical to the longitudinal spectral density (Sw/Su) is less than the canonical value of 4/3 (even less than 1) for all levels indicating anisotropic turbulence even at very small scales above the canopy. As a consequence, estimated values of TKE dissipation rate (ε) from the vertical component are smaller than those obtained from the horizontal velocity components. This finding has a direct influence on the applicability of classical Kansas spectral models valid for HHF terrain as well as on the budget of wind variances. Additionally, the behavior of the non‐dimensional gradient of mean wind speed is tested with regard to conformity to z‐less scaling requirements (i.e. linear dependence on stability). It is confirmed that a stability threshold (such as Rf > 0.25, where Rf is the flux Richardson number) is a stronger determinant of z‐less behavior than the existence of a well‐defined inertial subrange ‐ opposite to observations in the SBL over ideal flat surfaces. Finally, the local equilibrium between the production and destruction of TKE within the RSL and transition layer is analyzed.

Scaling, Anisotropy, and Complexity in Near‐Surface Atmospheric Turbulence

“…Although the value of this ratio is within the 20% margin of one and therefore could be considered almost constant (not shown), the individual values show a negative correlation with increasing complexity (apart from scaled temperature), indicating interestingly that the turbulence with a higher degree of horizontal small‐scale isotropy is found in more complex conditions (cf., anisotropy above canopy, Brugger et al, ). These results are also contrary to Babić and Rotach () where ε wu diverges more from one. In the stable regime where anisotropy was successful in improving scaling only in isotropic conditions, the mesoscale processes appear to be more important than in the unstable regime.…”

“…Here ε i is the dissipation rate as determined from the spectral density in the inertial subrange of the velocity component i . Babić and Rotach () have shown that over heterogeneous surfaces these ratios, particularly ε wu , can deviate strongly from one.…”

A TKE‐Based Framework for Studying Disturbed Atmospheric Surface Layer Flows and Application to Vertical Velocity Variance Over Canopies

“…The two experiments have been described in detail in the literature, and here we include only key information. Despite the inertial subrange slope observed in the longitudinal structure function, both data sets present large deviations from local isotropy at the scales sampled by the sonic anemometers as previously reported by Chamecki and Dias (2004) and Babić and Rotach (2018). Runs satisfying three criteria were selected for further analysis: azimuth wind direction within ±45 ∘ (in the frame of reference of the sonic anemometer), stationarity of the horizontal wind (Vickers & Mahrt, 1997), and the existence of an inertial subrange in the second-order structure function with slope within 10% of the theoretical prediction of 2∕3 (Kolmogorov, 1941).…”

Analysis of Dual Nature of Heat Flux Predicted by Monin‐Obukhov Similarity Theory: An Impact of Empirical Forms of Stability Correction Functions

“…If it is assumed that the condition Ri f > 0.25 is sufficient to filter out all the “non‐Kolmogorov turbulence” cases, the z ‐less concept appears to be valid and φ m can be taken as a linear function of ζ . However, in a recent study, Babic and Rotach () have pointed out that the existence of significant number of data points corresponds to “Kolmogorov turbulence” in the supercritical range ( Ri f > 0.25), suggesting a breakdown of the z ‐less regime.…”