Turbulence Spectra, Dissipation and Turbulent Kinetic Energy Budgets in the Stable Boundary Layer over Inhomogeneous Terrain

The turbulence characteristics of flows over heterogeneous and patchy vegetation still present an ongoing issue, mainly due to the lack of experimental results. In this study we focus on turbulence spectral characteristics, dissipation rate of turbulent kinetic energy (TKE) and budgets of the TKE in the wintertime, night-time boundary layer over inhomogeneous surface. Measurements from a tall mast which was situated in a small deciduous forest were analysed. Measurements at five levels above the canopy height (approximately h=18 m) were influenced by the upwind conditions which represent different types of surfaces. In this study we focus on the combined influence of the roughness sublayer (RSL) found above tall vegetation and the internal boundary layer (IBL).

Results showed that horizontal velocity spectra have the predicted -5/3 slope in the high-frequency range indicating the existence of the inertial subrange at the upper four levels (z>1.5h), but the same is not found for the vertical wind spectra. The lowermost level (2 m above the canopy) is clearly influenced by the roughness elements showing that on average there is no well-defined inertial subrange. Testing the local isotropy hypothesis more thoroughly resulted in a ratio of the horizontal spectral densities (Sv/Su) approaching the 4/3, while the ratio of the vertical to the longitudinal spectral density (Sw/Su) was less than 1 for all levels indicating an anisotropic turbulence above the canopy. The vertical velocity spectra have deviations for the inertial subrange and this is investigated in more detail.

We found that an appropriate stability function for the non-dimensional dissipation of TKE calculated from spectra in the inertial subrange differs from the classical linear function obtained for the Kansas data. We compared our results with the empirical models of Kaimal et al. (Q J R Meteorol Soc 98:563–589, 1972) and Olesen et al. (Boundary-Layer Meteorol 29: 285–312, 1984). Using Kaimal's model, normalized spectra show that -2/3 slope is followed quite closely for a wide range of frequencies in the inertial subrange. The stability has an important effect on turbulence spectral structure and also on frequencies of spectral peaks. Extending the analysis to the Olesen approach, normalized spectra collapse to one single curve. Finally, analysing the budget terms of the turbulent kinetic energy non-equilibrium conditions are found.