A dynamical model for urban heat islands

Effects of nonlinearity on the airflow past an urban heat island and precipitation change downwind, are investigated analytically in the context of the weakly nonlinear response of a stably stratified uniform flow to specified heating. The heating structure is assumed to be bell-shaped in the horizontal and exponentially decreasing with height. The forcing to the first-order equation exhibits cooling in the concentrated low-level heating region. The linear solution component shows upward motion downstream as suggested by many previous studies. The weakly nonlinear solution component shows downward or upward motion downstream depending on the heating depth. It is proposed that when the heating depth is large, but still within a valid range of the perturbation expansion, the linear and weakly nonlinear effects constructively work together to produce enhanced upward motion on the downstream side, not far from the heating centre. This explains to a greater extent the precipitation enhancement downstream of the heat island than is possible from the linear effect alone. It is also proposed that when the heating depth is small, the linear and weakly nonlinear effects destructively work together to reduce upward motion on the downstream side, not far from the heating centre. This explains to a greater extent the lack of precipitation enhancement downstream than is possible from the linear effect alone.