Generation of internal wave breathers by steady flow over an obstacle

In certain stratifications internal wave breathers can exist. Such stratifications include symmetric double-pycnocline continuous stratifications provided the two pycnoclines are sufficiently far apart. Here the generation of breathers by steady flow over a small obstacle is investigated using a two-dimensional non-hydrostatic primitive equation numerical model under the Boussinesq approximation. The symmetric stratification consists of two thin hyperbolic tangent pycnoclines which separate the fluid into three nearly constant density layers. The two pycnoclines have the same thickness and the same density jump across them. The upper and lower constant density layers have the same thickness. Nonlinear internal waves in this type of stratification can be modelled with the modified KdV (mKdV) equation. If the pycnoclines are far enough apart the cubic coefficient in the mKdV equation is positive and weakly-nonlinear theory predicts the existence of breathers. In this numerical study a large number of simulations have been undertaken, varying the speed of the upstream flow, the amplitude and width of the obstacle and the thickness of the upper and lower layers. Multiple upstream propagating internal wave breathers are generated in a small region of parameter space. Their formation appears to arise from nonlinear-interactions in the lee wave field downstream of the obstacle.