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

International audience ; 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 $k_x^{−1}$ range for the three components of the velocity vector: $E_u(k_x), E_v(k_x), E_w(k_x)\propto k_x^{-1}$ [as well as for the 1D temperature spectrum $E_{\theta}(k_x)\propto k_x^{-1}$]. This suggests the existence of strong wave turbulence. A necessary condition for strong wave turbulence to be manifest is that the flow direction wavenumber, $k_x$, extends to much lower values than the slope normal one, $k_z$. This is satisfied in the present field experiment where wave energy is injected at wavenumber $k_x=k_N=(N_a\sin\alpha)/\overline{u_j}$, while $k_z\sim 1/\Delta z$, with $N_a$ the ambient stratification, $\alpha$ the slope angle, $\overline{u_j}$ the maximum wind velocity, and $\Delta z$ the shear layer thickness of the jet. In the inertial range, the velocity spectra exhibit a power law $k_x^{−5/3}$ 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 $L_B$ that is close to the Dougherty–Ozmidov scale $L_{OZ}$. The high Reynolds number based on the Taylor micro-scale, $Re_{\lambda} \sim{ 10^3}$, allows clear identification of the spectral laws.