Abstract
We are presenting the results of a stability analysis of a background wind shear in the presence of stable stratification and of height dependent coefficients of eddy viscosity and eddy thermal conduction. It is shown that the vertical gradients of the eddy coefficients substantially affect the phase velocities, growth rates and vertical structure of the gravity wave and are responsible for the appearance of some counter-gradient heat fluxes and Reynolds stresses. It is suggested that these gradients may explain the observed counter-gradient fluxes in the stable atmospheric boundary layer.