The flow through the collector of a solar chimney power plant model on the roof of the Aerospace and Mechanical Engineering building at the University of Arizona was investigated numerically for the conditions of the experiment. The measured wall temperature and inflow velocity for a representative day were chosen for the simulation. The simulation was performed with a newly developed higher-order-accurate compact finite difference code. The code employs fifth-order-accurate biased compact finite differences for the convective terms and fourth-order-accurate central compact finite differences for the viscous terms. A fourth-order-accurate Runge-Kutta method was employed for time integration. Unsteady random disturbances are introduced at the inflow boundary and the downstream evolution of the resulting waves was investigated based on the Fourier transforms of the unsteady flow data. Steady azimuthal waves with a wavenumber of roughly four based on the channel half-height are the most amplified as a result of Rayleigh-Bénard-Poiseuille instability. Different from plane Rayleigh-Bénard-Poiseuille flow, these waves appear to merge in the streamwise direction. Oblique waves are also amplified. The growth rates are however lower than for the steady modes. Because of the strong streamwise flow acceleration, the growth rates decrease in the downstream direction.