调制Stokes波列长期演化过程中的熵值分析
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摘要
深水Stokes波列的不稳定调制演化与实际海面的瞬变性、波浪破碎、畸形波等海洋现象密切相关,且波列在长期演化的过程中,演化特性会随着时间尺度的增加而改变,前人的研究多是针对其空间分布特性,对于波列内部能量的分布和变化趋势尚不清楚,因此引入熵的概念用于描述调制Stokes波列长期演化过程中任意时刻波浪场中不同频率波浪能量分布的均匀性。通过高阶谱方法数值模型,模拟了不同初始波陡条件下调制Stokes波列波数谱熵值的长期演化,给出不同阶段初始波陡和熵的关系,并将稳定状态熵值及谱形与典型海浪谱进行对比分析,发现调制Stokes波列长期演化的波数谱熵值和谱形均趋向实测JONSWAP谱,表明其经过长期演化发展,谱变宽变连续,波场内的能量分布趋向均匀并保持动态的平衡,同时也更加趋近于真实海浪。
The evolution of modulated Stokes wave trains in deep water is closely related to the actual sea surface transitioning,the wave breaking and the occurrence of freak waves in the ocean.And in the process of long-term evolution,the evolution characteristics will change along with the increase of time scales.Previous research mainly focused on the spatial distribution characteristics,however,its inherent energy distribution and change trend are not clear.So the concept of entropy is used to describe the uniformity of wave energy distribution in wave field at any time in the long-term evolution of Stokes waves.Based on High Order Spectra Method numerical model,the long-term evolution of the entropy of modulated Stokes wave trains varying initial wave steepness is simulated and the relationship between initial wave steepness and entropy in different time scales is given.The stable spectrum shape and entropy are compared with the typical wave spectrum.It is found that the entropies and shapes are close to that of the measured JONSWAP.The results indicate that the wave number spectra shapes tend to be more intensive and continuous after the long-term evolution.The energy distribution in the wave field tends to be uniform and keeps dynamic balance.Wave trains develop to a statement that is similar to the real ocean waves.
The evolution of modulated Stokes wave trains in deep water is closely related to the actual sea surface transitioning,the wave breaking and the occurrence of freak waves in the ocean.And in the process of long-term evolution,the evolution characteristics will change along with the increase of time scales.Previous research mainly focused on the spatial distribution characteristics,however,its inherent energy distribution and change trend are not clear.So the concept of entropy is used to describe the uniformity of wave energy distribution in wave field at any time in the long-term evolution of Stokes waves.Based on High Order Spectra Method numerical model,the long-term evolution of the entropy of modulated Stokes wave trains varying initial wave steepness is simulated and the relationship between initial wave steepness and entropy in different time scales is given.The stable spectrum shape and entropy are compared with the typical wave spectrum.It is found that the entropies and shapes are close to that of the measured JONSWAP.The results indicate that the wave number spectra shapes tend to be more intensive and continuous after the long-term evolution.The energy distribution in the wave field tends to be uniform and keeps dynamic balance.Wave trains develop to a statement that is similar to the real ocean waves.
引文
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[16]Tao A F,Zheng J H,Mee Mee S,et al.Re-study on recurrence period of Stokes wave train with High Order Spectral method[J].Nanjing:China Ocean Engineering,2011,25(4):679-686.
[17]Tao A F,Zheng J H,Mee Mee S,et al.The Most Unstable Conditions of Modulation Instability[J].Beijing:Journal of Applied Mathematics,2012(1110-757X):335-351.
[18]Xiao W T,Liu Y M,Wu G,et al.Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution[J].USA:Journal of Fluid Mechanics,2013,720:357-392.
[19]Henderson K L,Peregrine D H,Dold J W.Unstedy water wave modulations:fully nonlinear solutions and comparison with the nonlinear Schr dinger equation[J].Holland:Wave Motion,1999,29:341-361.
[2]Benjamin T B,Hasselmann K.Instability of periodic wave trains in nonlinear dispersive systems[J].England:Proceedings of the Royal Society A Mathematical Physical&Engineering Sciences,1967,299(299):59-75.
[3]Longuethiggins M S.Modulation of the amplitude of steep wind-waves[J].USA:Journal of Fluid Mechanics,1980,99(4):705-713.
[4]Lake B M,Yuen H C,Rungaldier H,et al.Nonlinear deep-water waves:theory and experiment.Part 2.Evolution of a continuous wave train[J].USA:Journal of Fluid Mechanics,1977,83:49-74.
[5]Melville W K.The instability and breaking of deep-water waves[J].USA:Journal of Fluid Mechanics,1982,115(115):165-185.
[6]Melville W K.Wave modulation and breakdown[J].USA:Journal of Fluid Mechanics,1983,128(-1):489-506.
[7]Su M.Evolution of groups of gravity waves with moderate to high steepness[J].USA:Physics of Fluids,1982,25(12):2167-2174.
[8]Tulin M P,Marshall P,Waseda T,et al.Laboratory observations of wave group evolution,including breaking effects[J].USA:Journal of Fluid Mechanics,1999,378(1):197-232.
[9]Hwung H H,Hsiao S C.Observations on the evolution of wave modulation[J].England:Proceedings of the Royal Society of London,2007,463(2077):85-112.
[10]Chiang W S,Hwung H H.Steepness effect on modulation instability of the nonlinear wave train[J].USA:Physics of Fluids,2007,19(19):111-112.
[11]Tao A F,Zheng J H,Chen B T,et al.Properties of freak waves induced by two kinds of nonlinear mechanisms[C].Spain:CoastalEngineering Proceedings,2012,1(33):waves 73.
[12]Tao A F,Qi K R,Zheng J H,et al.The occurrence probabilities of rogue waves in different nonlinear stages[C].Korea:Coastal Engineering Proceedings,2014,1(34):waves 35.
[13]Zheng J H,Wang G,Dong G H,et al.Numerical study on Fermi-Pasta-Ulam-Tsingou problem for 1Dshallow-water waves[J].Holland:Wave Motion,2014,51(1):157-167.
[14]Alber I E.The effects of randomness on the stability of two-dimensional surface wave trains[J].England:Proceedings of the Royal Society A,1978,363(1715):525-546.
[15]Dommermuth D G,Yue D K P.A high-order spectral method for the study of nonlinear gravity waves[J].USA:Journal of Fluid Mechanics,1987,184:267-288.
[16]Tao A F,Zheng J H,Mee Mee S,et al.Re-study on recurrence period of Stokes wave train with High Order Spectral method[J].Nanjing:China Ocean Engineering,2011,25(4):679-686.
[17]Tao A F,Zheng J H,Mee Mee S,et al.The Most Unstable Conditions of Modulation Instability[J].Beijing:Journal of Applied Mathematics,2012(1110-757X):335-351.
[18]Xiao W T,Liu Y M,Wu G,et al.Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution[J].USA:Journal of Fluid Mechanics,2013,720:357-392.
[19]Henderson K L,Peregrine D H,Dold J W.Unstedy water wave modulations:fully nonlinear solutions and comparison with the nonlinear Schr dinger equation[J].Holland:Wave Motion,1999,29:341-361.