A new view of nonlinear water waves: the Hilbert spectrum

Creators: Huang, Norden E.; Shen, Zheng; Long, Steven R.

Abstract

We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

Additional Information

"Reprinted, with permission, from the Annual Review of Fluid Mechanics, Volume 31 copyright 1999 by Annual Reviews, www.annualreviews.org" The authors would like to thank Professors T. Y. Wu of the California Institute of Technology and O. M. Phillips of the Johns Hopkins University for their continuous guidance and encouragement over the years. We also would like to thank Professor Fred Browand of the University of Southern California for sharing the turbulent boundary data with us. NEH would like to thank Professor Wu especially for the hospitality extended to him during his sabbatical visit at Caltech. NEH and ZS are supported in part by grants from NSF (NSF-CMS-9615897), US Navy NSWC, and NASA RTOP program (622-47-11). SRL is supported in part by a NASA (N00014-98-F-0412) RTOP program (622-47-13). NASA has filed for a patent for the algorithms of the EMD and Hilbert spectral analysis methods.

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