An Analytical Study on the Urban Boundary Layer

A two-layer model based on the linearized time-independent atmospheric dynamical equations is proposed in this paper. The analytical solutions of the vertical, the horizontal motions and the potential temperature field induced by the anthropogenic source of urban surface heating are obtained, therefore the heat island circulation existing in unstable boundary layer is verified theoretically. From the analytical solutions, some conclusions can be drawn. (1) The vertical motion induced by urban heat island consists of two parts, namely, the cross-hill wave and the lee wave; (2) The cross-hill wave only exists in the unstable boundary layer, and varies with height according to exponential function law; (3) The vertical motion induced by heat island reaches the maximum at the top of the unstable boundary layer; (4) The wave generated by heat island not only propogates to the downwind district but also travels to the upwind area; (5) is not the necessary condition of the lee wave generation.