Nonlinear Internal Wave Properties Estimated with Moored ADCP Measurements

A method is developed to estimate nonlinear internal wave (NLIW) vertical displacement, propagation direction, and propagation speed from single moored acoustic Doppler current profiler (ADCP) velocity observations. The method is applied to three sets of bottom-mounted ADCP measurements taken on the continental slope in the South China Sea in 2006–07. NLIW vertical displacement is computed as the time integration of ADCP vertical velocity observations corrected with the vertical advection of the background flow by the NLIW. NLIW vertical currents displace the background horizontal current and shear by ~150 m. NLIW propagation direction is estimated as the principal direction of the wave-induced horizontal velocity vector, and propagation speed is estimated using the continuity equation in the direction of wave propagation, assuming the wave’s horizontal spatial structure and propagation speed remain constant as the NLIW passes the mooring, typically O(10 min). These NLIW properties are estimated simultaneously and iteratively using the ADCP velocity measurements, corrected for their beam-spreading effect. In most cases, estimates converge to within 3% after four iterations. The proposed method of extracting NLIW properties from velocity measurements is confirmed using NLIWs simulated by the fully nonlinear Dubreil–Jacotin–Long model. Estimates of propagation speed using the ADCP velocity measurements are also in good agreement with those calculated from NLIW arrival times at successive moorings. This study concludes that velocity measurements taken from a single moored ADCP can provide useful estimates of vertical displacement, propagation direction, and propagation speed of large-amplitude NLIWs.