Supplement to 'Third-order transport due to internal waves and non-local turbulence in the stably stratified surface layer'

A linear theory ofinternal grab ity kaves (IGWs) is applied to consider the IGW-induced \CrtiCal flUXeS Of kinetic energy, pressure and squared density (or buoyancy) in non-turbulent stable stratified fluid characterized by the Brunt-Vaisala frequency. N. These fluxes are required in modelling distant link,, and non-local transports in the atmosphere. Investigations of the vertical flux of kinetic energy have shown that this flux, caused by the wave component performing the most efficient vertical transport, is proportional to N-3. As far as the authors know. the flux of the squared density fluctuations as not systematically investigated. It is shown to be proportional to N-5.