A new mathematical model of the two-dimensional atmospheric boundary layer over undulating terrain is presented. Neither the hydrostatic assumption nor the Bousinesque as sumption need to be introduced in this model. The system of equation is described with orthogonal curvilinear coordinates, and one of the axes (ξ) coincides with the undulating ground surface. Then, the system of equations are expanded in the Fourier series of ξ and the time, following the spectral method. In this way, the equations can be reduced to a system of second order simultaneous ordinary differential equations.
The advantages of the model are as follows: (1) easy application to an arbitrarily un dulating ground surface, (2) the possibility of a precise discussion about a phenomenon with an appreciable vertical acceleration like a sea breeze front and (3) the elimination of com putational instability in the solutions by wave number truncation. An example of the calcu lated result for land and sea breeze circulation with our model suggests that the model could be used in a study of the other orographic environment.