The sensitivity of internal solitary waves to localized patches of mixing

While most theoretical work on internal waves idealizes the stratification, geophysical stratifications are typically much more complicated.  We build on recent work on nearly linear stratifications by adopting perturbations that take the form of a localized patch of mixing. We present a data-centric framework that seeks to identify which locations and widths of a mixing patch yield the largest effect on the structure of exact waves (computed via the Dubreil-Jacotin-Long equation), linear waves (computed via the longwave Taylor-Goldstein equation), and evolving nonlinear waves (via time-dependent simulations using the incompressible Navier-Stokes equations). We find that the vertical structure functions of linear waves are most sensitive to perturbations below (above) the pycnocline when the pycnocline is above (below) mid-depth; furthermore, as the pycnocline approaches mid-depth, the depth of the perturbation layer with the greatest impact approaches the depth of the pycnocline. In contrast, the centre streamwise velocity profile of a DJL wave is perturbed most by layers above (below) the pycnocline when the pycnocline is above (below) mid-depth. Finally, we present the results of simulations of evolving nonlinear waves, where we compare pairs of cases with and without a perturbation layer. Despite the presence of an initial patch of unstable fluid, the perturbation layer is sustained during the simulation; nevertheless, slight Rayleigh-Taylor instabilities are observed within and about the perturbation layer. Modulations in the horizontal velocity field about the leading solitary wave are compared with the results of the linear and DJL analyses.