Internal-Gravity wave propagation in a range-dependent waveguide with forcing at the bottom

We compute the propagation of waves forced at the bottom of an inhomogeneous stratified moving fluid, using vertical normal modes and horizontal rays. The problem is separated into a range-dependent nonlinear eigenproblem that defines the vertical structure of the solution and a set of coupled inhomogeneous ordinary differential equations with nonconstant coefficients in the horizontal. Under the adiabatic approximation, i.e. neglecting the energy transfer between different modes due to variation of the medium properties in the horizontal, the latter reduces to a set of uncoupled ODEs. Results of the implementation of the method are given in an idealized case.