Novel computational technique for studying atmospheric internal waves

This study investigates atmospheric internal waves, also known as gravity waves, which occur within a fluid medium rather than at its surface. The model is developed using shallow fluid theory, characterized by a set of nonlinear partial differential equations (PDEs). This approach is grounded in the assumption that the horizontal dimensions of the fluid are much larger than the vertical dimensions, making it suitable for representing atmospheric internal waves due to their significant horizontal extent. We introduce a novel iterative method to solve this model and conduct a convergence analysis of the proposed approach. The method, known as the Nonlinear Iterative Method (NIM), is a modification of the Adomian Decomposition Method (ADM), which eliminates the need for polynomials or discretization. The accuracy of the NIM is assessed by comparing the results with existing solutions from the literature, demonstrating its effectiveness and reliability in modeling atmospheric internal waves.