Shear-stress and temperature-flux cospectra in the convective atmospheric surface layer using matched asymptotic expansions

In our recent work we predicted the shear-stress and temperature-flux cospectra in the surface layer using the multi-point Monin-Obukhov similarity and dimensional analysis. In this work we predict these cospectra using matched asymptotic expansions employing their transport equations. The outer (large) scales are shown to have the mixed-layer scaling. As the wavenumber increases the scaling of the dominant terms in the cospectral equations change, resulting in a singular perturbation problem with two inner scales. Matched asymptotic expansions up to the second order are obtained as a solution, which gives the lead-order scaling of the cospectra in two scaling ranges and the corrections due to finite values of the scale separations.