Evidence of strong wave turbulence and of Bolgiano temperature spectra in katabatic winds on steep slopes

Abstract

The katabatic winds on steep slopes investigated in the present study reveal a novel spectral behavior, observed in the outer part of the jet. At low wavenumbers, the one-dimensional (1D) velocity spectra show evidence of a kx−1 range for the three components of the velocity vector: Eu(kx),Ev(kx),Ew(kx)∝kx−1 [as well as for the 1D temperature spectrum Eθ(kx)∝kx−1]. This suggests the existence of strong wave turbulence. A necessary condition for strong wave turbulence to be manifest is that the flow direction wavenumber, kx, extends to much lower values than the slope normal one, kz. This is satisfied in the present field experiment where wave energy is injected at wavenumber kx=kN=(Na sin α)/uj¯, while kz∼1/Δz, with Na the ambient stratification, α the slope angle, uj¯ the maximum wind velocity, and Δz the shear layer thickness of the jet. In the inertial range, the velocity spectra exhibit a power law kx−5/3 over two decades, whereas the temperature-buoyancy spectra show evidence of a −7/5 slope in the buoyancy sub-range, followed by a −5/3 slope. The change in spectral slopes occurs at the Bolgiano scale LB that is close to the Dougherty–Ozmidov scale LOZ. The high Reynolds number based on the Taylor micro-scale, Reλ∼103, allows clear identification of the spectral laws.