An advanced and intensive computational solution development is integrated with an asymptotic technique, to examine the impact of the combustion surface morphology on the generated rotational flow field in a solid rocket chamber with wide ranges of forcing frequencies. The simulated rectangular chamber is closed at one end and is open at the aft end. The upper and lower walls are permeable to allow steady and unsteady injected air to generate internal flow mimicking the flow field of the combustion gases in real rocket chamber. The frequencies of the unsteady injected flow are chosen to be very close or away from the resonance frequencies of the adapted chamber. The current study accounts for a wide range of wave numbers that reflect the complexity of real burning processes. Detailed derivation for Navier-Stokes equations at the four boundaries of the chamber is introduced in the current study. Qualitative comparison is performed with recent experimental work carried out on a two-inch hybrid rocket motor using a mixture of polyethylene and aluminum powder. The higher the percentage of aluminum powder in the mixture, the more the corrugations of the combustion surface. This trend is almost similar to the computational and analytical results of a simulated solid rocket chamber.