Lagrangian Transport by Vertically Bounded Internal Gravity Wavepackets

Horizontally propagating, vertically bounded internal wave modes induce both a horizontal Eulerian flow (EF) and a Stokes drift (SD) which, combined, result in the Lagrangian transport of fluid. Through theory, confirmed by numerical simulations, we predict the EF and SD are found for modes in arbitrary stratification. In the case of mode-1 waves in uniform stratification, we recover the mode-2 structures of the EF and SD originally predicted by McIntyre (J. Fluid Mech. 1973) including a singularity that results from a resonance occurring when the EF has phase speed equal to the group speed of the wavepacket. In top-hat stratification, the EF is not in itself a single mode. Consequently this singularity disappears and a new sequence of resonances are manifest as the induced flow resonates with higher order vertical modes. Generally, the vertically integrated EF and SD are each zero if the background density varies continuously. However, in the limit of a two-layer fluid, an interfacial wave induces an EF and SD whose vertical integrals are each non-zero but which together sum to zero. This singular behaviour occurs because a two-layer fluid does not permit higher order vertical modes.