We study the non-linear transient gravity waves inside vast oceans with general topographies. These waves are generated following climate variations simulated by an external pressure acting on the ocean's surface. We use a perturbation method for the study. The present approach necessitates a mild slope of the topography. Quadratic solutions are obtained from nonlinear theory technique and illustrated. The reliability of the nonlinear (quadratic) solution is examined by a comparison between the trace of the bottom and the lowest streamline. The proposed model is shown to be strongly efficient in simulating the considered phenomenon, especially if the slope of the topography is not sharp. The features of the phenomenon under consideration are revealed and discussed mathematically and physically according to the nonlinear theory technique.