A scaling law of internal run-up duration

Abstract

Wave tank experiments with long internal waves of elevation, of different initial length l, moving in a two-fluid system, interacting with a weak slope of 0.045 rad, show an onshore flow of the dense water, at the undisturbed pycnocline-slope intersection, of duration $11.3\sqrt{l/g'}$ (g′ reduced gravity). This period corresponds to that of a strong bottom current event measured in the stratified ocean at the Ormen Lange gas field, at 850 m depth, lasting for 24 hrs, corresponding to $11.2\sqrt{l/g'}$, using the width l = 300 km of the Norwegian Atlantic Current (NAC) at the site as length scale, suggesting a lateral sloshing motion of the NAC causing the event. The onshore velocity of the dense fluid has a maximal velocity of $0.4\sqrt{g'h_2}$ in laboratory and 0.5 ms$^{-1}=0.3\sqrt{g'h_2}$ in the field (h ₂ mixed upper layer thickness). Run-up of the dense fluid, beyond the undisturbed pycnocline-slope intersection, has initially a front velocity of $0.35\sqrt{g'h_2}$, corresponding to the velocity of the head of a density current on a flat bottom. Due to disintegration, an initially depressed pycnocline results in comparatively smaller run-up and velocity. While moving past the turning point, a dispersive wave train is formed in the back part of the depression wave, developing by breaking into a sequence of up to eight boluses moving by the undisturbed pycnocline-slope intersection.