The topographic variation underwater of the continental slope is one of the main causes for triggering off the formation of internal waves, and the continental slope internal waves are ubiquitous in the ocean. The horizontal variation of waveguide environment, caused by the internal wave and the continental slope, can lead to acoustic normal mode coupling, and then generate sound field fluctuation. Most of the existing research work focused on studying the effect of single perturbation factor of either the internal waves or the continental slope on acoustic mode coupling and intensity fluctuation, while it is hard to find some research work that takes into account both the internal waves and the topographic variations as influencing factors. In this work, numerical simulations for the sound waves to propagate through the internal waves in the downhill direction are performed by using the acoustic coupled normal-mode model in four waveguide environments: thermocline, internal wave, continental slope and continental slope internal wave. And the mode coupling and intensity fluctuation characteristics and their physical mechanisms are studied by comparing and analyzing the simulation results of the four different waveguide environment constructed. Some conclusions are obtained as follows. The intra-mode conduction coefficients are symmetric with respect to the center of the internal wave, while the inter-mode coupling coefficients are antisymmetric around it. As the sound waves propagate toward or away from the center of the internal wave, the acoustic mode coupling becomes enhanced or weakened, and the coupling coefficients curves for large mode oscillate. The influence of internal wave perturbation makes the energy transfer from the smaller modes to the larger modes, which increases the attenuation of sound field intensity. The number of the waveguide modes increases and the mode intensity attenuation decreases, when the sound waves propagate downhill. The total intensity of all modes for the continental slope internal wave environment is greater than for the internal wave environment and less than for the continental environment, and the energy transfer between mode groups is stronger than for individual effect of internal wave or continental slope, which leads more energy to transfer from the smaller to larger mode groups and the energy of the sound field above the thermocline to increase.