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研究生: 錢樺
Chien, Hwa
論文名稱: 方向波譜之推算及其應用於波能消散之研究
Estimation of Directional Spectra and Applications to the Study of Wave Dissipation
指導教授: 莊士賢
Chuang, Laurence Z. H.
高家俊
Kao, Chia Chuen
學位類別: 博士
Doctor
系所名稱: 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年: 2003
畢業學年度: 91
語文別: 英文
論文頁數: 157
中文關鍵詞: 方向波譜分析波能消散
外文關鍵詞: Directional spectral analysis, wave dissipation
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  • 波浪於其生成、成長、傳遞到碎波的演變過程中,在深水處的能量消散機制及其影響迄今尚未完全被了解。本文之目的在於探討波浪的能量消散現象及其特性。本文由分析實測波浪及氣象資料著手,先建立準確推算方向分佈的數值方法,再藉由實測波浪的方向分佈特性估算波浪能量消散率,探討波能消散特性。本文可分為兩個部分:第一部分為各種方向波譜推算數值方法之特性及其應用的比較研究,第二部分為波能消散率估算及當波浪傳遞速度遠高於海面風速時,波浪能量消散現象之探討。

    在相同的觀測數據下,應用不同的方向波譜推算方法會獲得差異甚大的結果。為確保方向分佈分析結果的正確性及準確性,本文建立傅立葉法、最大概似法、疊代最大概似法及擴展型最大熵法等五種方向波譜推算方法的計算程序,先以數值模擬方式比較上述方法在解析度、雜訊承受度及與觀測方式匹配的特性;再將這些方法分別應用於分析碟型資料浮標及波高儀陣列所觀測得之現場資料,了解各種分析方法於實務上的限制,並提出了進行波浪方向波譜觀測作業中儀器設計及觀測資料處理的建議。最後基於後續研究中對方向分佈準確性及高解析度的要求,本文選擇擴展型最大熵法作為方向波譜推算的方法。

    為探討波能消散特性,本文嘗試應用方向波譜估算波能消散率。本文以Phillips (1985)提出的平衡域理論為基礎,將理論中的方向分佈表示式取代為七股海上觀測樁波高儀陣列於現場觀測之分析結果,探討2001年冬季七股海域的波浪能量消散率特性。結果發現波浪消散率與海面上十米風速呈羃次相關,此結果與 Felizardo & Melville (1994) 觀測結果趨勢一致,但資料散亂程度較大。本文交叉比對與氣溫與海水表面溫度差值與波浪能量消散率,發現溫差範圍縮小時資料散亂程度相對減小,且當氣溫低於水溫越多時波浪能量消散率越大。

    現有大部分波浪推算模式中,風剪力授與波浪能量,波浪成長引致之白帽碎波為深水處波能消散的唯一考慮機制,為進一步探討是否存在其他影響,本文針對波浪傳遞速度遠高於海面風速,不存在白帽碎波的波浪,探討其能量消散現象。由於四個波非線性交互作用具有穩定譜形及在共振頻帶間轉移能量時同時影響方向分佈的特性,本文基於DIA數值推算結果,以正規化方向分佈寬度於頻率上的分佈特性為指標,定性上探討其波能消散特性。分析長期實測資料之方向分佈特性後,本文建立台灣西部海域方向分佈模式,並發現在海面風速相對波速十分小的情況下,波能仍會消散,消散量隨波浪尖銳度增加而變大,與波齡關係相較不明顯。此分析結果為波浪動量向上傳遞至大氣的現象提供了觀測上的證據。

    Wave dissipation is one of the least understood phenomena among the mechanisms involved in wave evolution. In deep water, the dissipation of surface waves can be regarded as results of interactions of the waves with upper-ocean surface turbulence. This turbulence can be recognized to be partly caused by wind stress resulting in whitecapping, and other sources of turbulences. In present study, accurate estimations of the directional spectra from field observations are used as diagnostic tools of investigating the wave dissipation. In order to ensure the obtaining of valid, accurate and high-resolution directional spectra, assessments of the up-to-date directional spectrum estimators are carried out. Analysis software based on the relevant theoretical foundations and testing procedures are established to evaluate and compare the performances, characteristics and biases of difference methods. As a result, the EMEM is considered to be the best choice considering the high-resolution potential, noise-robust capability and instrumentation effects. Moreover, the recommendations of the utilization of directional spectra estimators and the arrangement of instrumentations are proposed.

    With the attempt to use directional spectral parameters to estimate the total wave energy dissipation rate, concepts from Phillips (1985) equilibrium range theory are adopted. The directional spreading functions in Phillips’ theory have been replaced by the directional spreading obtained by the measurement from wave gauges array during the winter monsoons. The dissipation estimates by this approach are compared to the observations by Felizardo and Melville (1994). The results show similar dependence of the dissipation rate to the wind speed, which demonstrates the possibility to replace the directional spectral parameters instead of the external wind forcing parameters in the estimation of wave dissipation. Since the wave dissipation processes are dynamically related to the wave field itself, the use of wave spectral parameters is reasonable. Moreover, with the increasing In Situ measurements available, the accurate determination of directional spectra will help to improve the understanding of wave dissipation characteristics.

    To further investigate the minor mechanisms associated with dissipation, a directional spreading parameter is proposed in present study to indicate the strength of swell dissipation rate. The conceptual idea is that since the swell, which propagates in the celerity faster than the wind, gains no more energy input from the wind, the dissipation of the each spectral components are coupled and stabilized by quadruplet nonlinear interactions, which redistribute the remain energy in both frequency and direction domain. Consequently, a parameter, which can be derived from the relationship of the normalized directional spreading to the non-dimensional frequency, is deduced based on the instinct properties of quadruplet nonlinear interaction. It is proposed to be utilized as an indicator to the strength of the energy dissipation rate. Qualitative computations by using DIA scheme are carries out to verify the idea. The application of the indicator was then applied to the cases of swell decay using field observations. The results demonstrate that wave steepness is connected to its dissipation rate. The steeper the swell, the stronger rate of the dissipation can be yielded. The qualitative phenomenon of upward momentum transfer, which is predicted by models, but not herebefore observed, is identified.

    Abstract ii Contents v List of Figures viii List of Tables xi List of Major Symbols x 1. Introduction 1  1.1 Background 1  1.2 Research overview 5 2. State-of-the-Art Wave Dynamics 7  2.1 Spectral description 8  2.2 Wave spectral evolution 11   2.2.1 Energy radiative equation 12   2.2.2 Source functions 12   2.2.3 Wind input 13    2.2.3.1 Initial theories 13    2.2.3.2 Expression in WAM Cycle 3 14    2.2.3.3 Expression in SWAN 15    2.2.3.4 Expression in WAM Cycle 4 16   2.2.4 Non-linear wave-wave interactions 18   2.2.5 Wave energy dissipation 20 3. Description and Analysis of Directional Spectrum 24  3.1 Theoretical background of directional spectrum estimators 25   3.1.1 Directional spectra and Cross-Power-Spectrum-Density 25   3.1.2 Fourier Series Method 27   3.1.3 Maximum Likelihood Method 30   3.1.4 Iterative MLM 34   3.1.5 Extended Maximum Entropy Method 34   3.1.6 Bayesian Approach Method 40  3.2 Validation and comparison of directional spectrum estimators 45   3.2.1 Simulation of wave data 45    3.2.1.1 Simulation of time series of water surface elevation 46    3.2.1.2 Simulation of cross-power-spectrum-density matrix 48   3.2.2 Test setups 49    3.2.2.1 One-dimensional spectrum 50    3.2.2.2 Unimodal distribution 51    3.2.2.3 Bimodal and asymmetric distributions 51    3.2.2.4 Noise contamination 52    3.2.2.5 Gauge array layout 53   3.2.3 Test results and discussion 54    3.2.3.1 On the high-resolution potential 55    3.2.3.2 On the noise-robust capability 57    3.2.3.3 On the gauge number effects 58  3.3 Field data analysis 61   3.3.1 Platform equipped with wave gauges array 61   3.3.2 Heave-pitch-roll data buoy 63   3.3.3 Discussion 65  3.4 Conclusion and recommendations 67 4 Application of Directional Spectrum to Wave Dissipation Rate Estimation 86  4.1 Theoretical background of wave dissipation 86   4.1.1 Whitecapping induced dissipation 86   4.1.2 Measurement and estimation of wave dissipation 88   4.1.3 Wave dissipation of global importance 91   4.1.4 Wave directionality effects on the dissipation 92   4.1.5 Research objective 93  4.2 Wave dissipation rate estimation by directional spectrum analysis 94   4.2.1 Equilibrium range theory 94   4.2.2 Derivation of using field directional spectrum 97  4.3 Results and discussion 99   4.3.1 Data selection and preliminary data process 100   4.3.2 On the wind speed dependency 100   4.3.3 On the atmospheric stability 102 5 Detection of Swell Decay 106  5.1 Theoretical background 106   5.1.1 Motivation 106   5.1.2 Physical causation of dissipation 106    5.1.2.1 The inversion problem 107    5.1.2.2 Wave induced stress and its interactions with atmosphere 108   5.1.3 Research objective and strategy 113  5.2 Consequences for the wave action balance 115   5.2.1 Properties of the quadruplet nonlinear interactions 115    5.2.1.1 Spectral evolution 116    5.2.1.2 Spectral shape stabilization 116    5.2.1.3 Directional spreading 118   5.2.2 Computation of quadruplet nonlinear interaction 119    5.2.2.1 Numerical integration method 120    5.2.2.2 Discrete interaction approximation (DIA) 120   5.2.3 Numerical simulation 123  5.3 Field data analysis and discussion 125   5.3.1 Data selecting 125   5.3.2 Results and discussion 127    5.3.2.1 Bottom effects 127    5.3.2.2 The dependency on wave age and wave steepness 128 6 Concluding Remarks 138 Bibliography 143 Acknowledgements 153 Vita 154

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