The pressure disturbance of a nonlinear internal wave train

Abstract

Observations from a lander fixed to the seafloor over the continental shelf in 124 m of water provide highly resolved velocity measurements through nonlinear internal waves of elevation. From these measurements we determine, for the first time, the non-hydrostatic pressure disturbance ($p_{nh}$) in nonlinear internal waves. For near-bottom waves of elevation ranging in amplitude, $a$, from 12 to 33 m, the value of $p_{nh}$ evaluated at the seafloor changes sign from $\,{>}\,0$ to $\,{<}\,0$ and back in accordance with weakly nonlinear theory; peak values of $\vert p_{nh}\vert$ range from 25 to 90 N m$^{-2}$. The external hydrostatic pressure disturbance due to the surface displacement ($\eta_H$) is inferred from horizontal accelerations. For elevation waves, $\eta_H\,{<}\,0$; peak values range from 0.1 to 9 mm (1 to 90 N m$^{-2}$). The internal hydrostatic pressure perturbation ($p_{Wh}$), caused by isopycnal displacement, is inferred from measured streamlines and an ambient density profile. Its value at the seafloor is $\,{>}\,0$ for elevation waves; peak values range from 100 to 300 N m$^{-2}$. $\vert\eta_H\vert$ and seafloor values of $\vert p_{nh}\vert$, $p_{Wh}$ all increase monotonically with $a$. Since $\vert p_{nh}\vert$ and $p_{Wh}$ increase at roughly the same rate with $a$, no clear trend arises in the degree to which waves become more or less non-hydrostatic as $a$ changes.

A distinct bottom pressure signature is determined for bottom-trapped nonlinear waves of elevation, a wave train consisting of a sequence of positive pressure perturbations (dominated by $p_{Wh}$). By inference, a train of surface-trapped nonlinear internal waves of depression will consist of a sequence of negative pressure perturbations. A result of this analysis is that significant properties of the waves can be discerned from a simple adequately resolved bottom pressure measurement.