Estimating propagation speed and direction, and vertical displacement of second-mode nonlinear internal waves from ADCP measurements

Propagation speed and direction, and vertical displacement of the second-mode nonlinear internal waves (NLIWs) over the continental shelf of the East China Sea are estimated by applying the iterative method, previously validated only for the first-mode NLIWs, to the along-beam velocities measured with the standard acoustic Doppler current profiler (ADCP). Two ADCPs mounted in trawl-resistance bottom mounts were deployed in upward looking configurations on the seabed at stations spaced 7.4 km apart, perpendicular to isobaths of the continental slope. During the observation period of two days, two wave trains arrived at an interval of approximately one day, whereas the flow was dominated by the semi-diurnal internal tide with a diurnal modulation. The results of the iteration show that the second-mode NLIWs of the convex type propagate shoreward at a speed of 0.44 (0.36) m s⁻¹ at the offshore (onshore) station. The amplitude of the leading wave is estimated to be about 20 m at the offshore station, which is reduced to about 10 m at the onshore station. All the parameters agree remarkably well with those estimated independently from the backscatter signal of the ADCPs. The propagation time of 6.8 h estimated for the averaged propagation speed and direction is also consistent with a 6.9-h lag of the arrival time of the wave train between the two stations. In addition to the propagating features of the second-mode NLIWs, the iterative method reveals the wave-induced velocity associated with the radiation of short, small-amplitude first-mode waves from the second-mode NLIW, which has been observed only with shipboard echo sounders.