Abstract
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.
Highlights
In a previous paper, Ge and Liu (2007), we discussed the nonlinear interaction between the water waves and the overlying turbulent winds over a very short time scale, approximately 40 s
Unlike Ge and Liu (2007), which was focused on short-time wind-wave interaction patterns, the present investigation aims to describe the long-term statistical characteristics that have general meanings for the entire process of wave growth
10−1 freq (Hz) concentrated on studying the effects of the wind fluctuations, including the wave-induced components and the wind turbulence, on the growth of the wave field and the feedback they receive at the same time
Summary
In a previous paper, Ge and Liu (2007), we discussed the nonlinear interaction between the water waves and the overlying turbulent winds over a very short time scale, approximately 40 s. Two major conclusions were reached: a) the wavelet-based wave power spectrum can vary significantly over such a short time scale due to the wave’s linear and quadratic phase couplings with the wind fluctuations, and b) the wind-wave linear and quadratic (nonlinear) interactions facilitate a complex energy transfer pattern that dictates the local energy variation of both the waves and the wind fluctuations At this point we admit that such a likely structure of energy transfer, dynamically important over short times, does not necessarily have general meanings for the long-term characteristics of wave growth. Unlike Ge and Liu (2007), the time scale considered here is long enough to allow for a good use of the classic higher-order Fourier analysis
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