Resumen
The Hilbert-Huang Transform (HHT) is extended to the time series analysis of wave orbital velocities resulting from the superposition of waves propagating in different directions. On a theoretical basis, it is shown that an apparently chaotic velocity signal may result from the interaction of three or more waves, each one with its own period and direction of propagation. Such result is compatible with records of PUV instruments. The comparison between bivariate HHT with Fourier directional analysis shows several advantages of the former, such as identification of wave groups and non-linear interaction components.Referencias
Flandrin, P.; G. Rilling; and P. Gonçalves (2004). "Empirical mode decomposition as a filter bank", IEEE Signal Process. Lett, v. 11, p. 112-114. http://dx.doi.org/10.1109/LSP.2003.821662
Huang, N. E.; S. R. Long; and Z. Shen (1996). "The Mechanism for frequency downshift in nonlinear wave evolution". Adv. Appl. Mechanics, vol. 32, p. 59-115. http://dx.doi.org/10.1016/S0065-2156(08)70076-0
Huang, N.E.; Z. Shen; S.R. Long; M.L. Wu; H.H. Shih; Q. Zheng; N.C. Yen; C.C. Tung; and H.H. Liu (1998). "The empirical mode decomposition and Hilbert spectrum for non-stationary time series analysis". Proc. R. Soc. London A, 454: 903-995. http://dx.doi.org/10.1098/rspa.1998.0193
Huang, N.E. and Z. Wu (2008). "A review on Hilbert-Huang Transform: Method and its applications to geophysical studies". Rev. Geophysics, 46: 1-23. http://dx.doi.org/10.1029/2007RG000228
Longuet-Higgins, M.; R. J. Seymour; and S. Pawka (1981). "A compact representation of ocean wave directionality". Applied Ocean Research, vol.3, p. 105-112. http://dx.doi.org/10.1016/0141-1187(81)90099-7
Moura, T.G.R. (2010). Application of Hilbert-Huang Transform to study waves measured by PUV.
M.Sc. thesis. Federal University of Rio de Janeiro. (in Portuguese)
Phillips, O. M. (1958). "The equilibrium range in the spectrum of wind generated waves", J. Fluid Mech. vol. 2, p. 426-434. http://dx.doi.org/10.1017/S0022112058000550
Phillips, O. M. (1960). "On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions", J. Fluid Mech., v. 9:2, p. 193-217. http://dx.doi.org/10.1017/S0022112060001043
Rilling, G.; P. Fladrin; P. Gonçalves (2007). "Bivariate Empirical Mode Decomposition", IEEE Signal Processing Lett. p. 936-939. http://dx.doi.org/10.1109/LSP.2007.904710
Sharma, J.N. and R.G. Dean (1979). "Second-order directional seas and associated wave forces", Proc. Offshore Technology Conference, vol. 4, p. 2505-2514. http://dx.doi.org/10.4043/3645-MS
Tanaka, T. and D. P. Mandic (2007). "Complex empirical mode decomposition", IEEE Signal Process. Lett., vol. 14, no. 2, p. 101-104. http://dx.doi.org/10.1109/LSP.2006.882107
Yunchao, G,; S. Enfang & S. Zhengyan, (2008). "Comparison of EMD and Complex EMD in Signal Processing", Congress on Image and Signal Processing, IEEE, p. 141-145.