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Ann. Geophys., 26, 747-758, 2008
www.ann-geophys.net/26/747/2008/
© European Geosciences Union 2008
Long-term wave growth and its linear and nonlinear interactions with wind fluctuations
Z. Ge1 and P. C. Liu2
1Ecosystems Research Division, NERL, USEPA, 960 College Station Road, Athens, GA 30605, USA
2NOAA Great Lakes Environmental Research Laboratory, 2205 Commonwealth Blvd., Ann Arbor, MI 48105, USA
Abstract. Following Ge and Liu (2007), the simultaneously recorded time series of wave elevation and wind velocity are examined
for long-term (on Lavrenov's τ4-scale or 3 to 6 h) linear and nonlinear interactions between the wind fluctuations
and the wave field. Over such long times the detected interaction patterns should reveal general characteristics for
the wave growth process. The time series are divided into three episodes, each approximately 1.33 h long, to
represent three sequential stages of wave growth. The classic Fourier-domain spectral and bispectral analyses are
used to identify the linear and quadratic interactions between the waves and the wind fluctuations as well as between
different components of the wave field.
The results show clearly that as the wave field grows the linear interaction becomes enhanced and covers wider range
of frequencies. Two different wave-induced components of the wind fluctuations are identified. These components, one
at around 0.4 Hz and the other at around 0.15 to 0.2 Hz, are generated and supported by both linear and quadratic
wind-wave interactions probably through the distortions of the waves to the wind field. The fact that the
higher-frequency wave-induced component always stays with the equilibrium
range of the wave spectrum around 0.4 Hz and
the lower-frequency one tends to move with the downshifting of the primary peak of the wave spectrum
defines the partition of the primary peak and the equilibrium range of the wave spectrum,
a characteristic that could not be revealed by short-time wavelet-based analyses
in Ge and Liu (2007). Furthermore, these two wave-induced peaks of the wind spectrum appear to have different
patterns of feedback to the wave field.
The quadratic wave-wave interactions also are assessed using the auto-bispectrum
and are found to be especially active during the first and the third episodes.
Such directly detected wind-wave interactions, both linear and nonlinear, may complement the existing
theoretical and numerical models, and can be used for future model development and validation.
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