TY - JOUR

T1 - Identifying Higher-Order Interactions in Wave Time-Series

AU - Ewans, Kevin

AU - Christou, Marios

AU - Ilic, Suzana

AU - Jonathan, Philip

PY - 2021/4/1

Y1 - 2021/4/1

N2 - Reliable design and reanalysis of coastal and offshore structures require, among other things, characterization of extreme crest elevation corresponding to long return periods. Extreme crests typically correspond to focused wave events enhanced by wave-wave interactions of different orders - third-order, four-wave interactions dominating in deep water (Janssen, P. A. E. M., 2003, "Nonlinear Four-Wave Interactions and Freak Waves," J. Phys. Oceanogr., 33(4), pp. 863-884). Higher-order spectral (HOS) analysis can be used to identify wave-wave interactions in time-series of water surface elevation; trispectral analysis is needed to detect third-order, four-wave interactions. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum - the T- and V-trispectrum (with corresponding tricoherences), respectively. It is shown that the T-tricoherence is capable of detecting phase-locked four-wave interactions of the type f4 = f1 + f2 + f3 when these are simulated with simple sinusoids, but such interactions were not detected in HOS model simulations and field data. It is also found that high V-tricoherence levels are detected at frequencies at which four-wave interactions of the type f1 + f2 = f3 + f4 are expected, but these may simply indicate combinations of independent pairs of Fourier components that happen to satisfy the frequency relationship. Preliminary analysis shows that using a cumulant-based trispectrum (Kravtchenko-Berejnoi, V., Lefeuvre, F., Krasnosel'skikh, V. V., and Lagoutte, D., 1995, "On the Use of Tricoherent Analysis to Detect Nonlinear Wave-Wave Interactions," Signal Process., 42(3), pp. 291-309) may improve identification of wave-wave interactions. These results highlight that caution needs to be exercised in interpreting trispectra in terms of specific four-wave interactions occurring in sea states and further research is needed to establish whether this is in fact possible in practice.

AB - Reliable design and reanalysis of coastal and offshore structures require, among other things, characterization of extreme crest elevation corresponding to long return periods. Extreme crests typically correspond to focused wave events enhanced by wave-wave interactions of different orders - third-order, four-wave interactions dominating in deep water (Janssen, P. A. E. M., 2003, "Nonlinear Four-Wave Interactions and Freak Waves," J. Phys. Oceanogr., 33(4), pp. 863-884). Higher-order spectral (HOS) analysis can be used to identify wave-wave interactions in time-series of water surface elevation; trispectral analysis is needed to detect third-order, four-wave interactions. Four-wave interactions between Fourier components can involve interactions of the type where f1 + f2 + f3 = f4 and where f1 + f2 = f3 + f4, resulting in two definitions of the trispectrum - the T- and V-trispectrum (with corresponding tricoherences), respectively. It is shown that the T-tricoherence is capable of detecting phase-locked four-wave interactions of the type f4 = f1 + f2 + f3 when these are simulated with simple sinusoids, but such interactions were not detected in HOS model simulations and field data. It is also found that high V-tricoherence levels are detected at frequencies at which four-wave interactions of the type f1 + f2 = f3 + f4 are expected, but these may simply indicate combinations of independent pairs of Fourier components that happen to satisfy the frequency relationship. Preliminary analysis shows that using a cumulant-based trispectrum (Kravtchenko-Berejnoi, V., Lefeuvre, F., Krasnosel'skikh, V. V., and Lagoutte, D., 1995, "On the Use of Tricoherent Analysis to Detect Nonlinear Wave-Wave Interactions," Signal Process., 42(3), pp. 291-309) may improve identification of wave-wave interactions. These results highlight that caution needs to be exercised in interpreting trispectra in terms of specific four-wave interactions occurring in sea states and further research is needed to establish whether this is in fact possible in practice.

KW - higher-order spectral analysis

KW - ocean waves and associated statistics

KW - offshore safety and reliability

KW - probability and spectral wave modeling

U2 - 10.1115/1.4047930

DO - 10.1115/1.4047930

M3 - Journal article

AN - SCOPUS:85090507970

VL - 143

JO - Journal of Offshore Mechanics and Arctic Engineering

JF - Journal of Offshore Mechanics and Arctic Engineering

SN - 0892-7219

IS - 2

M1 - 021201

ER -