Evaluation of velocity-related approximations in the nonlinear shallow water equations for the Kuril Islands, 2006 tsunami event at Honolulu, Hawaii

Abstract

[1] The Nonlinear Shallow Water Equations (NSWE) provide a model for long wave behavior commonly used in tsunami modeling problems in which the scale associated with the surface wavelength is much greater than the ocean depth. This approximation allows for the derivation of the NSWE under the assumptions that the pressure is hydrostatic and the horizontal velocity components uniform along the water column. The present study uses current velocity data acquired by the Kilo Nalu Near-Shore Reef Observatory Acoustic Doppler Current Profiler (ADCP) on the south shore of Oahu (21.288°N, 157.865°W) in the aftermath of the 2006 Kuril tsunami to assess the validity of the NSWE assumptions on the velocity components. ADCP measurements provide information on all three velocity components along the water column, allowing the calculation of terms discarded in the NSWE approximation, containing temporal or vertical derivatives. Comparison of the relative magnitude of terms retained and neglected in the NSWE reveals that in shallow waters (10 m) the size of discarded terms remains smaller, but approaches the order of magnitude of retained terms in the momentum equations. Not all terms present in the equations can be evaluated from the available data, so verification of the assumptions investigated here represents a necessary but not sufficient condition for the validity of the NSWE approximation to model tsunami waves in shallow coastal waters.