On the '-1' scaling of air temperature spectra in atmospheric surface layer flows

Abstract:

The spectral properties of scalar turbulence at high wavenumbers have been extensively studied in turbulent flows, and existing theories explaining the k^–5/3 scaling within the inertial subrange appear satisfactory at high Reynolds numbers. Equivalent theories for the low wavenumber range have been comparatively lacking because boundary conditions prohibit attainment of such universal behavior. A number of atmospheric surface layer (ASL) experiments reported a k^–1 scaling in air temperature spectra E_TT(k) at low wavenumbers but other experiments did not. Here, the occurrence of a k^–1 scaling in E_TT(k) in an idealized ASL flow across a wide range of atmospheric stability regimes is investigated theoretically and experimentally. Experiments reveal a k^–1 scaling persisted across different atmospheric stability parameter values (ζ) ranging from mildly unstable to mildly stable conditions (–0.1< ζ < 0.2). As instability increases, the k^–1 scaling vanishes. Based on a combined spectral and co-spectral budget models and upon using a Heisenberg eddy viscosity as a closure to the spectral flux transfer term, conditions promoting a k^–1 scaling are identified. Existence of a k^–1 scaling is shown to be primarily linked to an imbalance between the production and dissipation rates of half the temperature variance. The role of the imbalance between the production and dissipation rates of half the temperature variance in controlling the existence of a ‘-1’ scaling suggests that the ‘-1’ scaling in E_TT(k) does not necessarily concur with the ‘-1’ scaling in the spectra of longitudinal velocity E_uu(k). This finding explains why some ASL experiments reported k^–1 in E_uu(k) but not E_TT(k). It also differs from prior arguments derived from directional-dimensional analysis that lead to simultaneous k^–1 scaling in E_uu(k) and E_TT(k) at low wavenumbers in a neutral ASL.