A spectral model for stably stratified turbulence

A solution of the inviscid rapid distortion equations for a stratified flow with homogeneous shear is proposed, extending the work of Hanazaki & Hunt (J. Fluid Mech., vol. 507, 2004, pp. 1–42) to the two horizontal velocity components. The analytical solution allows for the determination of the spectral tensor evolution at any given time starting from a known initial condition. By following the same approach as that adopted by Mann (J. Fluid Mech., vol. 273, 1994, pp. 141–168), a model for the spectral velocity tensor in the atmospheric boundary layer is obtained, where the spectral tensor, assumed to be isotropic at the initial time, evolves until the breakup time where the spectral tensor is supposed to achieve its final state observed in the boundary layer. The model predictions are compared with atmospheric measurements obtained over a forested area, giving the opportunity to calibrate the model parameters, and further validation is provided by additional low-roughness data. Characteristic values of the model coefficients and their dependence on the Richardson number are proposed and discussed.