The k^-1 scaling of air temperature spectra in atmospheric surface layer flows

A number of atmospheric surface layer (ASL) experiments reported a k-1 scaling in air temperature spectra ETT(k) at low wavenumber k but other experiments did not. Occurrence of this scaling law in ETT(k) in an idealized ASL flow across a wide range of atmospheric stability regimes is investigated theoretically and experimentally using measurements collected above a lake and a grass surface. 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 simplified spectral and co-spectral budgets and using a Heisenberg eddy viscosity as a closure to the spectral flux transfer term, conditions promoting a k-1 scaling in ETT(k) 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. When -0.1 < ζ < 0.2, such imbalance exhibits weak dependence on ζ and hence z, which is shown to be the main cause for a -1 scaling at low k. As the atmosphere becomes more unstable, the imbalance determined from experiments here are not significantly affected by ζ, thereby negating conditions promoting a -1 scaling in ETT(k). 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 ETT(k) does not necessarily concur with the -1 scaling in the spectra of longitudinal velocity Euu(k). This finding explains why some ASL experiments reported k-1 in Euu(k) but not in ETT(k).

Duke Scholars

Author Gabriel G. Katul Civil and Environmental Engineering