Estimating wave elevation from pressure using second order nonlinear wave-wave interaction theory with applications to Hurricane Andrew

We present a methodology to determine the nonlinear relationship between an observed dynamic pressure time series at a fixed point below the surface a nd the surface elevation. This method extends the formalism of previous stu dies where the analytical relationship between surface elevation and potent ial in both unidirectional and directional irregular wave trains has been d erived up to second order in wave steepness. Laboratory wave tank tests sho w that the predicted wave elevation from the nonlinear model is more accura te than the predicted linear surface elevation of a transient irregular wav e train, especially for deep troughs and high wave crests. We apply the nonlinear theory of estimate, wave elevation of a unique press ure time series recorded at a site 20 km south of Terrebonne Bay, Louisiana , during Hurricane Andrew and compare that result to the wave elevation est imated from the same time series using linear wave theory. The site was wit hin 30 km of the storm's eye at closest approach. The maximum significant w ave height using nonlinear wave theory is reduced by 8.4% to 7.69 m. The no nlinear interaction is seen to be. strongest during the six-hour period tha t hurricane force winds were present at the site.