Perturbed potential temperature field in the atmospheric boundary layer

This article discusses the modeling of perturbed potential temperature field in an atmospheric boundary layer (ABL). We adopt a convection–diffusion model with specified initial and boundary conditions that resulted from simplifying the linearized equation of the standard continuity equation for potential temperature field in the state of weak turbulent fluxes. By implementing the method of separation of variables to the nonsteady-state perturbed potential temperature, we obtain a regular Sturm–Liouville boundary value problem (BVP) for the spatial-dependent, vertical distribution component of the perturbed potential temperature. By transforming the problem in the canonical form into the Liouville normal form, we provide asymptotic solutions for the corresponding second-order BVP using the Wentzel–Kramers–Brillouin (WKB) theory. We further observe a remarkable qualitative agreement between the asymptotic solutions and numerical simulations. As other convection–diffusion models typically perform, the perturbed potential temperature diminishes and approaches the steady-state condition over an extended period of time.