Time-dependent non-reflecting boundary conditions for simulations of wave propagation in geophysical shear flows

In numerical simulations of wave propagation in fluids, one often needs to apply non-reflecting boundary conditions or radiation conditions at the outflow boundary to prevent wave reflections. This thesis examines time-dependent radiation conditions for modeling the propagation of atmospheric gravity waves and Rossby waves.;The results are compared with those obtained by simply setting the fluid variables to zero at boundary or applying a steady radiation condition and are found to be more stable and to more accurately represent the exact solutions. A nonlinear correction to the time-dependent radiation condition is also developed and implemented.;The radiation condition is written in terms of a Laplace convolution integral, so it is non-local in time and expensive to compute, requiring values of the dependent variable at all previous time levels. The convolution integral is approximated so as to make the computations local in time and hence less expensive.