Energy transport by nonlinear internal waves

Winter stratification on Oregon’s continental shelf often produces a near-bottom layer of dense fluid that acts as an internal waveguide upon which nonlinear internal waves propagate. Shipboard profiling and bottom lander observations capture disturbances that exhibit properties of internal solitary waves, bores, and gravity currents. Wavelike pulses are highly turbulent (instantaneous bed stresses are 1 N m−2), resuspending bottom sediments into the water column and raising them 30+ m above the seafloor. The wave cross-shelf transport of fluid often counters the time-averaged Ekman transport in the bottom boundary layer. In the nonlinear internal waves that were observed, the kinetic energy is roughly equal to the available potential energy and is O(0.1) megajoules per meter of coastline. The energy transported by these waves includes a nonlinear advection term 〈uE〉 that is negligible in linear internal waves. Unlike linear internal waves, the pressure–velocity energy flux 〈up〉 includes important contributions from nonhydrostatic effects and surface displacement. It is found that, statistically, 〈uE〉 ≃ 2〈up〉. Vertical profiles through these waves of elevation indicate that up(z) is more important in transporting energy near the seafloor while uE(z) dominates farther from the bottom. With the wave speed c estimated from weakly nonlinear wave theory, it is verified experimentally that the total energy transported by the waves is 〈up〉 + 〈uE〉 ≃ c〈E〉. The high but intermittent energy flux by the waves is, in an averaged sense, O(100) watts per meter of coastline. This is similar to independent estimates of the shoreward energy flux in the semidiurnal internal tide at the shelf break.