| We examine the transmission of internal gravity waves through non-uniformly stratified fluid using piecewise-linear theory and fully nonlinear numerical simulations. Transmission coefficients are measured using the ratio of the flux of transmitted to incident pseudoenergy, T. An analytic prediction of T is found for waves tunnelling through a piecewise-linear shear flow in which the fluid is unstratified over the depth of the shear and uniformly stratified elsewere. In weak shear, transmission across critical layers, where the phase speed of waves matches the flow speed, is possible if the background density profile is continuous. For a discontinuous background density profile no transmission occurs through critical layers, however, transmission values increase at other phase speeds. Numerical simulations of wavepackets show little dependence of transmission values on wavepacket extent and a significant increase in transmission values for larger initial wave amplitudes. |
