混合浪中长波对短波的调制研究
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摘要
海浪是一种常见的海洋现象，通常指一种小尺度海洋表面重力波，包含风浪和涌浪。可将其看作一系列振幅和相位均不相同的随机简单波动的叠加。
海浪在海洋遥感和小尺度海气相互作用中扮演重要角色。中小尺度的短波是海表粗糙度的主要成份。小尺度粗糙度可影响电磁波在海表面的散射。涌浪、内波以及锋面等造成的非均匀流场对于海面小尺度粗糙度有调制作用，这种调制作用也是这些海洋现象微波遥感的基础。通常，使用水动力调制传递函数描述涌浪对短波的影响。有关短波调制的研究对于海洋遥感和海气相互作用意义重大。尽管前人在理论和观测中都获得了不少成就，但是目前对于该调制机制和规律的认识还存在很多问题。
为观察短波被长波的调制情况，在实验室产生混合浪并测量波面位移数据。使用本征模态分解法(IMD)方法分析混合浪波面位移数据。与经验模态分解(EMD)方法相比，IMD方法避免了模态混淆。将混合浪数据分解为若干本征模态函数。许多数据最高频本征模态频率范围非常接近，这反映了即使外界条件不同，仍然存在某一特定频率的波动。
对比风浪中不同尺度的三个本征模态：风浪主要波、中等波与小尺度波，分析长波对它们的作用。将每个长波周期均分为8个小的位相区间，计算各本征模态在各小区间内的均方位移，以此代表某一模态的能量沿长波的分布。风浪主要波、小尺度波和介于二者之间的中等尺度波，其能量沿长波位相的分布具有不同特征。风浪主要波的能量随长波波陡增加而减少，其分布与长波同相且关于长波波谷对称。中等尺度波的能量则随长波波陡增加而增加，在长波波峰迎风面略微高于背风面。小尺度风浪的能量随着风速和长波波陡的增加而增加，随着风区长度的增加而减少，在长波波峰迎风面明显高于背风面。风浪能量分布在长波波峰迎风面高于背风面，具有不对称特征。这一特征主要由小尺度波的能量分布体现。考虑能使短波能量分布发生相移的各种影响因素，结合观测，可以认为长波遮拦效应是导致短波能量分布不对称的主要原因。
长波的轨道流场导致了多普勒效应。对于给定波数，短波表观频率在长波一周期内经过加权平均的值相对于固有频率产生了净降低量。在长波不同位相，同样的表观频率对应的固有频率不同。分析短波谱的调制传递函数随波数的变化，结果显示，最高频模态内各种尺度的短波，其所受调制几乎不随波数变化。如此一来，最高频模态所受调制可代表其包含的各种尺度的小波所受的调制。
对现有调制模式和相关理论综合分析的基础上，考虑了长波通过风应力对小波的影响，提出了一个新的理论调制模型。模型结果显示，对于传播方向与风向相同的波浪，短波能量的最大值位于长波波峰迎风面；对于高频小波，其调制随波数变化不大。
The Study of Modulation of Short Waves by the Long WavesAbstract
Wave is a normal phenomenon on the ocean and it affects the living of humandirectly.Usually it is the name of surface gravity wave concluding swell and windwaves which are relatively short.And it could be seen as a sum of waves of differentphases and amplitudes.
Waves play an important role in ocean remote sensing and air-sea interaction.Ocean surface roughness of ocean is contributed mostly by intermediate and smallscale surface waves.The non-uniform flows caused by some phenomenon such asswells and fronts could modulate small-scale roughness.And this modulation is alsothe foundation of the microwave remote sensing to these phenomenon.Hydrodynamicmodulation transfer function is used to describe the effect of long waves to the shortwaves.The research about wave modulation is very important.During severaldecades a lot of improvements have been made and a lot of important facts are found.However the mechanism of wave modulation is not well understood yet.
Experiments were conducted in the laboratory to observe the modulation of shortwind waves by mechanically generated monochromatic long waves.The surfaceelevations as well as the surface gradients are measured.Some alterations are made tothe Empirical Mode Decomposition (EMD) approach to avoid the blending ofIntrinsic Mode Function (IMF).In the altered mode decomposition approach,the IMFdecomposition is done in frequency space instead of in time domain.With this method,every surface elevation record is decomposed into a few IMFs.The high frequencyIMFs of the same ordinal number extracted from different wave records have almostidentical frequency ranges,therefore represent the surface undulations of a particularfrequency scale under different wave conditions.The squared elevations of each high frequency IMF are phase averaged to find its variation along the long wave profile.Itis found that the energy of high frequency waves are asymmetry on the surface oflong wave,with its maximum occurs at the upwind quadrants of the long wave crests.In view of the different phase shifts induced by various modulation mechanisms,together with the above observations,we credit the asymmetric distribution ofsmall-scale wave energy on long wave profile mainly to the wind sheltering effect oflong waves.
The orbital velocity provide a background current to the short waves.And theDoppler effects should be noticed when the wave number spectrum are transferred tothe frequency spectrum.The advection of the wave number component by the orbitalcurrent of background waves produces a net downshift in the encounter frequency.
After some theoretical analysis of recent modulation model and mechanisms,anew modulation model is made.This model connects wind stress to the spectrum ofshort waves.And calculation results from this model show that when a train of longwave travels with the wind,the maximums of short wave spectrum occurs at theupwind quadrants of the crests of the long wave.And the modulation of the shortwave changes little with the wave numbers.
海浪在海洋遥感和小尺度海气相互作用中扮演重要角色。中小尺度的短波是海表粗糙度的主要成份。小尺度粗糙度可影响电磁波在海表面的散射。涌浪、内波以及锋面等造成的非均匀流场对于海面小尺度粗糙度有调制作用，这种调制作用也是这些海洋现象微波遥感的基础。通常，使用水动力调制传递函数描述涌浪对短波的影响。有关短波调制的研究对于海洋遥感和海气相互作用意义重大。尽管前人在理论和观测中都获得了不少成就，但是目前对于该调制机制和规律的认识还存在很多问题。
为观察短波被长波的调制情况，在实验室产生混合浪并测量波面位移数据。使用本征模态分解法(IMD)方法分析混合浪波面位移数据。与经验模态分解(EMD)方法相比，IMD方法避免了模态混淆。将混合浪数据分解为若干本征模态函数。许多数据最高频本征模态频率范围非常接近，这反映了即使外界条件不同，仍然存在某一特定频率的波动。
对比风浪中不同尺度的三个本征模态：风浪主要波、中等波与小尺度波，分析长波对它们的作用。将每个长波周期均分为8个小的位相区间，计算各本征模态在各小区间内的均方位移，以此代表某一模态的能量沿长波的分布。风浪主要波、小尺度波和介于二者之间的中等尺度波，其能量沿长波位相的分布具有不同特征。风浪主要波的能量随长波波陡增加而减少，其分布与长波同相且关于长波波谷对称。中等尺度波的能量则随长波波陡增加而增加，在长波波峰迎风面略微高于背风面。小尺度风浪的能量随着风速和长波波陡的增加而增加，随着风区长度的增加而减少，在长波波峰迎风面明显高于背风面。风浪能量分布在长波波峰迎风面高于背风面，具有不对称特征。这一特征主要由小尺度波的能量分布体现。考虑能使短波能量分布发生相移的各种影响因素，结合观测，可以认为长波遮拦效应是导致短波能量分布不对称的主要原因。
长波的轨道流场导致了多普勒效应。对于给定波数，短波表观频率在长波一周期内经过加权平均的值相对于固有频率产生了净降低量。在长波不同位相，同样的表观频率对应的固有频率不同。分析短波谱的调制传递函数随波数的变化，结果显示，最高频模态内各种尺度的短波，其所受调制几乎不随波数变化。如此一来，最高频模态所受调制可代表其包含的各种尺度的小波所受的调制。
对现有调制模式和相关理论综合分析的基础上，考虑了长波通过风应力对小波的影响，提出了一个新的理论调制模型。模型结果显示，对于传播方向与风向相同的波浪，短波能量的最大值位于长波波峰迎风面；对于高频小波，其调制随波数变化不大。
The Study of Modulation of Short Waves by the Long WavesAbstract
Wave is a normal phenomenon on the ocean and it affects the living of humandirectly.Usually it is the name of surface gravity wave concluding swell and windwaves which are relatively short.And it could be seen as a sum of waves of differentphases and amplitudes.
Waves play an important role in ocean remote sensing and air-sea interaction.Ocean surface roughness of ocean is contributed mostly by intermediate and smallscale surface waves.The non-uniform flows caused by some phenomenon such asswells and fronts could modulate small-scale roughness.And this modulation is alsothe foundation of the microwave remote sensing to these phenomenon.Hydrodynamicmodulation transfer function is used to describe the effect of long waves to the shortwaves.The research about wave modulation is very important.During severaldecades a lot of improvements have been made and a lot of important facts are found.However the mechanism of wave modulation is not well understood yet.
Experiments were conducted in the laboratory to observe the modulation of shortwind waves by mechanically generated monochromatic long waves.The surfaceelevations as well as the surface gradients are measured.Some alterations are made tothe Empirical Mode Decomposition (EMD) approach to avoid the blending ofIntrinsic Mode Function (IMF).In the altered mode decomposition approach,the IMFdecomposition is done in frequency space instead of in time domain.With this method,every surface elevation record is decomposed into a few IMFs.The high frequencyIMFs of the same ordinal number extracted from different wave records have almostidentical frequency ranges,therefore represent the surface undulations of a particularfrequency scale under different wave conditions.The squared elevations of each high frequency IMF are phase averaged to find its variation along the long wave profile.Itis found that the energy of high frequency waves are asymmetry on the surface oflong wave,with its maximum occurs at the upwind quadrants of the long wave crests.In view of the different phase shifts induced by various modulation mechanisms,together with the above observations,we credit the asymmetric distribution ofsmall-scale wave energy on long wave profile mainly to the wind sheltering effect oflong waves.
The orbital velocity provide a background current to the short waves.And theDoppler effects should be noticed when the wave number spectrum are transferred tothe frequency spectrum.The advection of the wave number component by the orbitalcurrent of background waves produces a net downshift in the encounter frequency.
After some theoretical analysis of recent modulation model and mechanisms,anew modulation model is made.This model connects wind stress to the spectrum ofshort waves.And calculation results from this model show that when a train of longwave travels with the wind,the maximums of short wave spectrum occurs at theupwind quadrants of the crests of the long wave.And the modulation of the shortwave changes little with the wave numbers.
引文
[1]Unna D T．Sea waves．Nature，1947，159： 239-242
[2]Longuet-Higgins M S and Stewart R W．Changes in the form of short gravity waves on long waves and tidal currents．J．Fluid Mech．，1960，8： 565-583
[3]Garrett C，Smith J．On the interaction between long and short surface waves．Phys．Oceanogr．，1976，6：925-930．
[4]Longuet-Higgins M S．The propagation of short surface waves on longer gravity waves．J．Fluid Mech．，1987，177： 293-306
[5]Henyey F S，Creamer D B，Dysthe R L，Scult R L，Wright J A．The energy and action of small waves riding on large waves．J．Fluid Mech．，1988，189：443-462
[6]Phillips O M．The dispersion of short wavelets in the presence of a dominant long wave．J ．Fluid Mech．，1981，107：465-485
[7]袁业立，黄谔，Donelan M A．论骑行波—Ⅰ．波动不稳定性和频率调制。中国科学(B辑)，1994，24(3)： 317-324
[8]侯建军，乐嘉春，戴世强．骑行波的非线性演化方程。力学季刊，2000，Vol．21 No．1：102-109
[9]安淑萍，乐嘉春，戴世强．有限深水中骑行波的显式Hamilton描述。力学季刊，2002，Vol．23 No．3：331-336
[10]Masson D．On the nonlinear coupling between swell and wind waves．J．Phys．Oceanogr．，1993，23：249-58
[11]Longuet-Higgins M S and Stewart R W．Radiation stresses in water waves： A physical discussion with applications．Deep Sea Res．，1964，11：527～562
[12]Phillips O M．The Dynamics of the Upper Ocean．New York： Cambridge University Press，1966： 56～63
[13]Wright J W，Plant W J，Keller W C and Jones W L．Ocean wave-radar modulation transfer functions from the west coast experiment．J．Geophys．Res．，1980，85(C9)： 4957～4966
[14] Miller S J, Shemdin O M and Longuet-Higgins M S. Laboratory measurements of modulation of short-wave slopes by long surface waves. J. Fluid Mech., 1991, 233:389-404
[15] Chen G, Belcher S E. Effects of long waves on wind generated waves. J. Phys. Oceanogr., 2000, 30: 2246-2256
[16] Kudryavtsev V N and Makin V K. Coupled dynamics of short waves and the airflow over long surface waves. J. Geophys. Res., 2002, 107(C12), 3209, doi: 10.1029/2001JC001251
[17] Hara T, K A Hanson, E J Bock and B Mete Uz. Observation of hydrodynamic modulation of gravity-capillary waves by dominant gravity waves. J. Geophys. Res., 2003, 108(C2),3028, doi: 10.1029/2001JC001100
[18] Violante-Carvalho N, F J Ocampo-Torres, I S Robinson. Buoy observations of the influence of swell on wind waves in the open ocean. Applied Ocean Research, 2004, 26: 49-60
[19] 王伟,沈正.短波特征的实验及理论解释.中国科学(D期),1998,28(6): 511-517
[20] Hwang P A. Phase Distribution of Small-Scale Ocean Surface Roughness. J. Phys. Oceanogr., 2002, 32: 2977-2987
[21] Kudryavtsev V N, Makin V K and Chapron B. Coupled sea surface-atmosphere model 2.Spectrum of short wind waves. J. Geophys. Res., 1999, 104(C4), 7625-7639
[22] Pierson W J and L Moskowitz. A proposed spectral form for full developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res., 1964, 69: 5181-5190
[23] Hasselmann K et al. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogr. Z., suppl. A., 1973, 8(12): 95pp
[24] Donelan M A, J Hamilton and W H Hui. Directional spectra of wind-generated waves. Philos. Trans. R. Soc. London, 1985, A315: 509-562
[25] Hwang P A and D W Wang. Directional distributions and mean square slopes in the equilibrium and saturation ranges of the wave spectrum. J. Phys. Oceanogr., 2001, 31:1346-1360.
[26] Hwang P A. A study of the wave number spectra of short water waves in the ocean. part 2: Spectral model and mean square slope. J. Atmos. Ocean. Technol., 1997, 14: 1174-1186
[27] Plant W J and J W Wright. Growth and equilibrium of short gravity waves in a wind-wave tank. J. Fluid Mech., 1977, 82: 767-793
[28] Donelan M A. The effect of swell on the growth of wind waves. APL Tech. Dig., 1987, 8: 18-23
[29] Hwang P A and O H Shemdin. The dependence of sea surface slope on atmospheric stability and swell conditions. J. Geophys. Res., 1988, 93: 903-912
[30] Cox C S and W Munk. Statistics of the. sea surface derived from sun glitter. J. Mar. Res., 1954, 13: 198-227
[31] Tang S and O H Shemdin. Measurement of high frequency waves using a wave follower. J.Geophys. Res., 1983, 88: 9832-9840
[32] Hwang P A and D W Wang. An empirical investigation of source term balance of small scale surface waves. J. Geophys. Res. Lett., 2004, 31, LI 5301, doi:10.1029/2004GL020080.
[33] Hwang P A. Wave number spectrum and mean-square slope of intermediate-scale ocean surface waves. J. Geophys. Res., 2005, 110, C10029, doi: 10.1029/2005JC003002
[34] Hwang P A. Observations of swell influence on ocean surface roughness. J. Geophys. Res., 2008a, 113, C12024, doi: 10.1029/2008JC005075
[35] Hwang P A, M A Sletten and J V Toporkov. Breaking wave contribution to low grazing angle radar backscatter from the ocean surface. J. Geophys. Res., 2008b, 113, C09017, doi: 10.1029/2008JC004752
[36] Hwang P A. Doppler frequency shift in ocean wave measurements: Frequency downshift of a fixed spectral wave number component by advection of wave orbital velocity. J. Geophys. Res., 2006, 111, C06033, doi: 10.1029/2005JC003072
[37] Keller W C and Wright J W. Microwave scattering and straining of wind-generated waves. Radio Sci., 1975, 10: 139-147
[38] Hughes B A. The Effect of Internal Waves on Surface Wind Waves 2: Theoretical Analysis. J. Geophys. Res., 1978, 83(C1): 455-465.
[39] Thompson D R, B L Gotwols and R E Sterner II. A comparison of measured surface-wave spectral modulations with predictions from a wave-current interaction model. J. Geophys. Res., 1988, 93 (C10): 12339-12343
[40] Alpers W and K Hasselmann. The two-frequency microwave technique for measuring ocean wave spectra from an airplane or satellite. Bound.-Layer Meteor., 1978, 13: 215-230
[41] Alpers W. Theory of radar imaging of internal waves. Nature, 1985, 314(6008): 245-247
[42] Hwang P A, Shemdin O H. Modulation of short waves by surface currents-A numerical solution. J. Geophys Res., 1990, 95: 16311-16318
[43] The Wise Group: Cavaleri L, AlvesJ-H G M, Ardhuin F, Babanin A, Banner M, Belibassakis K, Benoit M, Donelan M, Groeneweg J, Herbers T H C, Hwang, P, Janssen P A E M, Janssen T, Lavrenov I V, Magne R, Monbaliu J, Onorato M, Polnikov V, Resio D, Rogers W E, Sheremet A, McKee Smith J, Tolman H L, van Vledder G, Wolf J, Young I. Wave modeling: The state of the art. Progress in Oceanography, 2007, 75(4): 603-674
[44] Jeffreys H. On the formation of waves by wind. Proceedings of the Royal Society A , 1924: 107:189-206
[45] Jeffreys H. On the formation of waves by wind. II. Proceedings of the Royal Society A., 1925, 110:341-147
[46] Phillips O M. On the generation of waves by turbulent wind. Journal of Fluid Mechanics, 1957,2:417-445
[47] Miles J.W.. On the generation of surface waves by shear flows. Journal of Fluid Mechanics , 1957,3: 185-204
[48] Dobson F W. Measurements of atmospheric pressure on wind-generated sea waves. Journal of Fluid Mechanics, 1971, 48: 91
[49] Snyder R L. A field study of wave-induced pressure fluctuation above surface gravity waves. Journal of Marine Research, 1974, 32: 497-531
[50] Snyder R L, Dobson F W, Elliott J A, Long R B. Array measurements of atmospheric pressure fluctuations above surface gravity waves. Journal of Fluid Mechanics, 1981, 102: 1-59
[51] Hasselmann D E, Bosenberg J. Field measurements of wave-induced pressure over wind sea and swell. Journal of Fluid Mechanics, 1991, 230: 391-428.
[52] Gent P R, Taylor P A. A numerical model of the air flow above water waves. Journal of Fluid Mechanics, 1976, 77: 105-128
[53] Makin V K, Chalikov D V. Numerical modeling of air structure above waves. Izvestiya Akademii Nauk SSSR, Atmosphere Ocean Physics, 1979, 15: 292-299 (Engl. transl.:Izvestiya Atmospheric and Oceanic Physics, 15, 199-204)
[54] Riley D S, Donelan M A, Hui W H. An extended Miles' theory for wave generation by wind. Boundary-Layer Meteorology, 1982, 22: 209-225
[55] Al-Zanaidi M A, Hui W H. Turbulent air flow water waves. Journal of Fluid Mechanics, 1984, 148:225-246
[56] Jacobs S J. An asymptotic theory for the turbulent flow over a progressive water wave. Journal of Fluid Mechanics, 1987, 174:69-80
[57] Chalikov D V, Makin V K. Models of the wave boundary layer. Boundary-Layer Meteorology, 1991, 56: 83-99
[58] Chalikov D V, Belevich M Y. One-dimensional theory of the wave boundary layer. Boundary-Layer Meteorology, 1993, 63: 65-96
[59] Van Duin C A, Janssen P A E M. An analytic model of the generation of surface gravity waves by turbulent air flow. Journal of Fluid Mechanics, 1992, 236: 197-215
[60] Nikolayeva Y I, Tsimring L S. Kinetic model of the wind generation of waves by a turbulent wind. Izvestiya Russian Academy of Sciences, Izvestiya Atmospheric and Oceanic Physics, 1986, 22: 102-107
[61] Belcher S E, Hunt J C R. Turbulent shear flow over slowly moving waves. Journal of Fluid Mechanics, 1993,251: 109-148
[62] Donelan M A. The dependence of the aerodynamic drag coefficient on wave parameters. Proceedings of the First International Conference on Meteorological and Air/sea Interaction of the Coastal Zone. American Meteorology Society, Boston, MA, 1982: 381-387 pp
[63] Smith S D, Anderson R J, Oost W A, Kraan C, Maat N, DeCosmo J, Katsaros K B,Davidson K L, Bumke K, Hasse L, Chadwick H M. Sea surface wind stress and drag coefficients: the HEXOS results. Boundary-Layer Meteorology, 1992, 60: 109-142
[64] Drennan W M, Graber H C, Donelan M A. Evidence for the effects of swell and unsteady winds on marine wind stress. Journal of Physical Oceanography, 1999a, 29: 1853-1864
[65] Oost W A, Komen G J, Jacobs C M J, van Oort C. New evidence for a relation between wind stress and wave age from measurements during ASGAMAGE. Boundary-Layer Meteorology, 2002, 103: 409-438
[66] Fabrikant A L. Quasilinear theory of wind-wave generation. Izvestiya. Atmospheric and Oceanic Physics, 1976, 12: 524-526
[67] Janssen P A E M. Quasilinear approximation for the spectrum of wind-generated water waves. Journal of Fluid Mechanics, 1982, 117: 493-506
[68] Janssen P A E M. Wave-induced stress and the drag of air flow over sea waves. Journal of Physical Oceanography, 1989, 19: 745-754
[69] Makin V K, Kudryavstev V N, Mastenbroek C. Drag of the sea surface. Boundary-Layer Meteorology, 1995,73: 159-182
[70] Donelan M A, Drennan W M, Terray E A. Wave number spectra of wind waves in the range of 1-50 m. In: Banner, M.L. (Ed.), The Wind-Driven Air-Sea Interface. School of Mathematics, The University of New South Wales, Sydney, 1999: 35-42pp
[71] Tsimring L Sh. Induced scattering of surface wind waves. Izvestiya Atmospheric and Oceanic Physics, 1983, 19:47-50
[72] Johnson A K, Hojstrup J, Vested H J, Larsen S E. On the dependence of sea surface roughness on wind waves. Journal of Physical Oceanography, 1998, 28 (9): 1702-1716
[73] Lange B, Johnson H K, Larsen S, Hojstrup J, Kofoed-Hansen H, Yelland M J. On detection of a wave age dependency for the sea surface roughness. Journal of Physical Oceanography, 2004,34(6): 1441-1458
[74] Hwang P A. Temporal and spatial variation of the drag coefficient of a developing sea under steady wind-forcing. Journal of Geophysical Research, 2005, 110, C07024,doi: 10.1029/2005 JC002912.
[75] Kasilingam D P, O H Shemdin. The validity of the composite surface model and its application to the modulation of radar backscatter. International Journal of Remote Sensing, 1992, 13(11): 2079-2104
[76] Longuet-Higgins M S. The effect of nonlinearities on statistical distributions in the theory of sea waves. J. Fluid Mech., 1963, 17: 459-480
[77] BARBER N F. The directional resolving power of an array of wave detectors. In: Ocean wave spectra Prentice Hall, Englewood Cliffs, NJ, 1963: 137-250pp
[78] Long R B, and K Hasselmann. A variational technique for extracting directional spectra from multi-component wave data. Journal of Physical Oceanography, 1979, 9(2): 373-381pp
[79] J(?)hne B K, and K S Riemer. Two-dimensional wave number spectra of small-scale water surface waves. J. Geophys. Res., 1990, 95(11): 531-546
[80] Trokhimovski Y G, V G Irisov, E R Westwater, L S Fedor and V E Leuski. Microwave polarimetric measurements of the sea surface brightness temperature from a blimp during the Coastal Ocean Probing Experiment (COPE). Journal of Geophysical Research, 2000, 105(C3): 6501-6516
[81] Feindt F, Schr(?)ter J, Alpers W. Measurement of the ocean wave-radar modulation transfer function at 35 GHz from a sea-based platform in the North Sea. Journal of Geophysical Research, 1979, 91(C8): 9701-9708
[82] Keller W C and W J. Plant Cross sections and modulation transfer functions at L-Band Ku-Bands measured during the TOWARD experiment．J．Geophys．Res．，1990： 95(C9)16277～16289
[83]Hara T，E J Bock and D．Lyzenga．In situ measurements of capillary-gravity wave spectra using a scanning slope gauge and microwave radars．J．Geophys．Res，1994，99：12593～12602
[84]丁赟．风浪状态对海面风应力的影响[硕士学位论文]．青岛：中国海洋大学，2005
[85]吕红民，许金山．大型风浪水槽风浪统计特征的测量和分析．青岛海洋大学学报(自然科学版)，1996，26(4)： 431～438
[86]吕红民，曹露洁，许金山．大型风浪水槽风速分布的测量和分析．青岛海洋大学学报自然科学版，1996，26(1)： 17～23
[87]Kolmogorov A N．Dissipation of energy in a locally isotropic turbulence．Doklady Akad．Nauk．SSSR，1941，32： 141
[88]Taylor G I．The spectrum of turbulence，Proceedings Royal Society London，Series A，1938，164：476～490
[89]Edson J B，C W Fairall，P G Mestayer and S E Larsen．A study of the inertial-dissipation method for computing air-sea fluxes．J．Geophys．Res．，1991，96：10689～10711
[90]Large W G and Pond S．Open ocean momentum flux measurements in moderate to strong winds．J．Phys．Oceanogr．，1981，11：324～336
[91]Fairall C W，J B Edson，S E Larsen and P G Mestayer．Inertial-dissipation air-sea flux measurements： A prototype system using real time spectral computations．J．Atmos．Oceanic Technol．，1990，7： 425～453
[92]文圣常，宇宙文．海浪原理与计算原理．北京：科学出报社，1984
[93]徐德伦，余定勇．随机海浪理论．北京：高等教育出版社，2001
[94]张立振．快速滤波本征模态信号分解及其在海洋数据分析中的应用[博士学位论文]．青岛：中国海洋大学，2006
[95]Cooley and Tukey．An Algorithm for the Machine Calculation of Comples Fourier series． Mathematics of Computation, 1965, 19(90)
[96] Cooley J W, Lewis PAW and Welch P D. The fast Fourier transform and its application. IEEE transactions on education, 1969, 12(1)
[97] Littlewood J E and R E A C Paley. Theorems on Fourier series and power series. J. London Math. Soc, 1931,6:230-233
[98] Calder(?)n A P and Zygmund A. On the existence of certain singular integrals. Acta. Math., 1952,88:85-139
[99] Stein E M. Singular integrals and differentiability properties of functions. N. J. : Princeton Univ. Press., 1970
[100] STEIN WEISS. Introduction to Fourier Analysis on Euclidean Spaces. N. J.: Princeton Univ. Press., 1971
[101] Coifman R. A real variables characterization of H p. Studia Math., 1974, 51: 269-274
[102] Coifman R R. A real variable characterization of Hp. Studia Math., 1974, 51: 547-598
[103] Latter R. A decomposition of Hp (Rn) in term of atoms. Studia Math., 1977, 62: 92-101
[104] Calderon A P. An atomic decomposition of distributions in parabolic H spaces. Adv. in math., 1977,25:216-225
[105] Peetre J. New thought on Besov spaces. Duke Univ. Math., Series, 1976
[106] Battle G et al.. A phase cell cluster expansion for Euclidian field theories. Ann. of Physics., 1982,142:95-1391
[107] Meyer Y. Principed incertitude. Bases hilbertinnes et al gebra d'operataur. Seminaire Bourbaki, 1985-1986
[108] Lemarie P and Meyer Y. On delete set bases Hilhertiennes. Revista. Mathmatica. Ibero. American A., 1986,2(1): 1-18
[109] Daubechies. The Wavelet transform: Time-Frquency Localizaion and Signal Analysis. IEEE Trans, On Information Theory, 1990, 36(5)
[110] 崔锦泰著[美].小波分析导论.西安交通大学出版社,1995
[111]Huang N E，Long S R and Shen Z．The mechanism for frequency downshift in nonlinear wave evolution．Adv．Appl．Mech．，1996，32： 59～111
[112]Huang N E，Shen Z，Long S R，Wu M C，Shih H H，Zheng Q，Yen N C，Tung C C and Liu H H．The empirical mode decomposition method and the Hilbert spectrum for nonlinear and non-stationary time series analysis．Proc．R Soc．Land．A．，1998，454： 903～995
[113]Huang N E，Shen Z and Long S R．A new view of nonlinear water waves： the Hilbert spectrum．A．Rev．Fluid Mech．，1999，31：417～457
[114]Huang N E，Wu M C，Long S R，Shen S S，P Qu，W Gloersen P and Fan K L．A confidence limit for the empirical mode decomposition and Hilbert spectra analysis，Proc．R．Soc．Land A．，2003，459： 2317～2345
[115]徐德伦．海洋随机数据分析[中国海洋大学研究生讲义]．2006
[116]Alpers W and I Hennings．A Theory of the Imaging Mechanism of Underwater Bottom Topography by Real and Synthetic Aperture Radar．J．Geophys．Res．，1984，89(C6)：10529～10546
[117]Plant W J．A Relationship Between Wind Stress and Wave Slope．J．Geophys．Res．，1982，87： 1961～1967
[2]Longuet-Higgins M S and Stewart R W．Changes in the form of short gravity waves on long waves and tidal currents．J．Fluid Mech．，1960，8： 565-583
[3]Garrett C，Smith J．On the interaction between long and short surface waves．Phys．Oceanogr．，1976，6：925-930．
[4]Longuet-Higgins M S．The propagation of short surface waves on longer gravity waves．J．Fluid Mech．，1987，177： 293-306
[5]Henyey F S，Creamer D B，Dysthe R L，Scult R L，Wright J A．The energy and action of small waves riding on large waves．J．Fluid Mech．，1988，189：443-462
[6]Phillips O M．The dispersion of short wavelets in the presence of a dominant long wave．J ．Fluid Mech．，1981，107：465-485
[7]袁业立，黄谔，Donelan M A．论骑行波—Ⅰ．波动不稳定性和频率调制。中国科学(B辑)，1994，24(3)： 317-324
[8]侯建军，乐嘉春，戴世强．骑行波的非线性演化方程。力学季刊，2000，Vol．21 No．1：102-109
[9]安淑萍，乐嘉春，戴世强．有限深水中骑行波的显式Hamilton描述。力学季刊，2002，Vol．23 No．3：331-336
[10]Masson D．On the nonlinear coupling between swell and wind waves．J．Phys．Oceanogr．，1993，23：249-58
[11]Longuet-Higgins M S and Stewart R W．Radiation stresses in water waves： A physical discussion with applications．Deep Sea Res．，1964，11：527～562
[12]Phillips O M．The Dynamics of the Upper Ocean．New York： Cambridge University Press，1966： 56～63
[13]Wright J W，Plant W J，Keller W C and Jones W L．Ocean wave-radar modulation transfer functions from the west coast experiment．J．Geophys．Res．，1980，85(C9)： 4957～4966
[14] Miller S J, Shemdin O M and Longuet-Higgins M S. Laboratory measurements of modulation of short-wave slopes by long surface waves. J. Fluid Mech., 1991, 233:389-404
[15] Chen G, Belcher S E. Effects of long waves on wind generated waves. J. Phys. Oceanogr., 2000, 30: 2246-2256
[16] Kudryavtsev V N and Makin V K. Coupled dynamics of short waves and the airflow over long surface waves. J. Geophys. Res., 2002, 107(C12), 3209, doi: 10.1029/2001JC001251
[17] Hara T, K A Hanson, E J Bock and B Mete Uz. Observation of hydrodynamic modulation of gravity-capillary waves by dominant gravity waves. J. Geophys. Res., 2003, 108(C2),3028, doi: 10.1029/2001JC001100
[18] Violante-Carvalho N, F J Ocampo-Torres, I S Robinson. Buoy observations of the influence of swell on wind waves in the open ocean. Applied Ocean Research, 2004, 26: 49-60
[19] 王伟,沈正.短波特征的实验及理论解释.中国科学(D期),1998,28(6): 511-517
[20] Hwang P A. Phase Distribution of Small-Scale Ocean Surface Roughness. J. Phys. Oceanogr., 2002, 32: 2977-2987
[21] Kudryavtsev V N, Makin V K and Chapron B. Coupled sea surface-atmosphere model 2.Spectrum of short wind waves. J. Geophys. Res., 1999, 104(C4), 7625-7639
[22] Pierson W J and L Moskowitz. A proposed spectral form for full developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res., 1964, 69: 5181-5190
[23] Hasselmann K et al. Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogr. Z., suppl. A., 1973, 8(12): 95pp
[24] Donelan M A, J Hamilton and W H Hui. Directional spectra of wind-generated waves. Philos. Trans. R. Soc. London, 1985, A315: 509-562
[25] Hwang P A and D W Wang. Directional distributions and mean square slopes in the equilibrium and saturation ranges of the wave spectrum. J. Phys. Oceanogr., 2001, 31:1346-1360.
[26] Hwang P A. A study of the wave number spectra of short water waves in the ocean. part 2: Spectral model and mean square slope. J. Atmos. Ocean. Technol., 1997, 14: 1174-1186
[27] Plant W J and J W Wright. Growth and equilibrium of short gravity waves in a wind-wave tank. J. Fluid Mech., 1977, 82: 767-793
[28] Donelan M A. The effect of swell on the growth of wind waves. APL Tech. Dig., 1987, 8: 18-23
[29] Hwang P A and O H Shemdin. The dependence of sea surface slope on atmospheric stability and swell conditions. J. Geophys. Res., 1988, 93: 903-912
[30] Cox C S and W Munk. Statistics of the. sea surface derived from sun glitter. J. Mar. Res., 1954, 13: 198-227
[31] Tang S and O H Shemdin. Measurement of high frequency waves using a wave follower. J.Geophys. Res., 1983, 88: 9832-9840
[32] Hwang P A and D W Wang. An empirical investigation of source term balance of small scale surface waves. J. Geophys. Res. Lett., 2004, 31, LI 5301, doi:10.1029/2004GL020080.
[33] Hwang P A. Wave number spectrum and mean-square slope of intermediate-scale ocean surface waves. J. Geophys. Res., 2005, 110, C10029, doi: 10.1029/2005JC003002
[34] Hwang P A. Observations of swell influence on ocean surface roughness. J. Geophys. Res., 2008a, 113, C12024, doi: 10.1029/2008JC005075
[35] Hwang P A, M A Sletten and J V Toporkov. Breaking wave contribution to low grazing angle radar backscatter from the ocean surface. J. Geophys. Res., 2008b, 113, C09017, doi: 10.1029/2008JC004752
[36] Hwang P A. Doppler frequency shift in ocean wave measurements: Frequency downshift of a fixed spectral wave number component by advection of wave orbital velocity. J. Geophys. Res., 2006, 111, C06033, doi: 10.1029/2005JC003072
[37] Keller W C and Wright J W. Microwave scattering and straining of wind-generated waves. Radio Sci., 1975, 10: 139-147
[38] Hughes B A. The Effect of Internal Waves on Surface Wind Waves 2: Theoretical Analysis. J. Geophys. Res., 1978, 83(C1): 455-465.
[39] Thompson D R, B L Gotwols and R E Sterner II. A comparison of measured surface-wave spectral modulations with predictions from a wave-current interaction model. J. Geophys. Res., 1988, 93 (C10): 12339-12343
[40] Alpers W and K Hasselmann. The two-frequency microwave technique for measuring ocean wave spectra from an airplane or satellite. Bound.-Layer Meteor., 1978, 13: 215-230
[41] Alpers W. Theory of radar imaging of internal waves. Nature, 1985, 314(6008): 245-247
[42] Hwang P A, Shemdin O H. Modulation of short waves by surface currents-A numerical solution. J. Geophys Res., 1990, 95: 16311-16318
[43] The Wise Group: Cavaleri L, AlvesJ-H G M, Ardhuin F, Babanin A, Banner M, Belibassakis K, Benoit M, Donelan M, Groeneweg J, Herbers T H C, Hwang, P, Janssen P A E M, Janssen T, Lavrenov I V, Magne R, Monbaliu J, Onorato M, Polnikov V, Resio D, Rogers W E, Sheremet A, McKee Smith J, Tolman H L, van Vledder G, Wolf J, Young I. Wave modeling: The state of the art. Progress in Oceanography, 2007, 75(4): 603-674
[44] Jeffreys H. On the formation of waves by wind. Proceedings of the Royal Society A , 1924: 107:189-206
[45] Jeffreys H. On the formation of waves by wind. II. Proceedings of the Royal Society A., 1925, 110:341-147
[46] Phillips O M. On the generation of waves by turbulent wind. Journal of Fluid Mechanics, 1957,2:417-445
[47] Miles J.W.. On the generation of surface waves by shear flows. Journal of Fluid Mechanics , 1957,3: 185-204
[48] Dobson F W. Measurements of atmospheric pressure on wind-generated sea waves. Journal of Fluid Mechanics, 1971, 48: 91
[49] Snyder R L. A field study of wave-induced pressure fluctuation above surface gravity waves. Journal of Marine Research, 1974, 32: 497-531
[50] Snyder R L, Dobson F W, Elliott J A, Long R B. Array measurements of atmospheric pressure fluctuations above surface gravity waves. Journal of Fluid Mechanics, 1981, 102: 1-59
[51] Hasselmann D E, Bosenberg J. Field measurements of wave-induced pressure over wind sea and swell. Journal of Fluid Mechanics, 1991, 230: 391-428.
[52] Gent P R, Taylor P A. A numerical model of the air flow above water waves. Journal of Fluid Mechanics, 1976, 77: 105-128
[53] Makin V K, Chalikov D V. Numerical modeling of air structure above waves. Izvestiya Akademii Nauk SSSR, Atmosphere Ocean Physics, 1979, 15: 292-299 (Engl. transl.:Izvestiya Atmospheric and Oceanic Physics, 15, 199-204)
[54] Riley D S, Donelan M A, Hui W H. An extended Miles' theory for wave generation by wind. Boundary-Layer Meteorology, 1982, 22: 209-225
[55] Al-Zanaidi M A, Hui W H. Turbulent air flow water waves. Journal of Fluid Mechanics, 1984, 148:225-246
[56] Jacobs S J. An asymptotic theory for the turbulent flow over a progressive water wave. Journal of Fluid Mechanics, 1987, 174:69-80
[57] Chalikov D V, Makin V K. Models of the wave boundary layer. Boundary-Layer Meteorology, 1991, 56: 83-99
[58] Chalikov D V, Belevich M Y. One-dimensional theory of the wave boundary layer. Boundary-Layer Meteorology, 1993, 63: 65-96
[59] Van Duin C A, Janssen P A E M. An analytic model of the generation of surface gravity waves by turbulent air flow. Journal of Fluid Mechanics, 1992, 236: 197-215
[60] Nikolayeva Y I, Tsimring L S. Kinetic model of the wind generation of waves by a turbulent wind. Izvestiya Russian Academy of Sciences, Izvestiya Atmospheric and Oceanic Physics, 1986, 22: 102-107
[61] Belcher S E, Hunt J C R. Turbulent shear flow over slowly moving waves. Journal of Fluid Mechanics, 1993,251: 109-148
[62] Donelan M A. The dependence of the aerodynamic drag coefficient on wave parameters. Proceedings of the First International Conference on Meteorological and Air/sea Interaction of the Coastal Zone. American Meteorology Society, Boston, MA, 1982: 381-387 pp
[63] Smith S D, Anderson R J, Oost W A, Kraan C, Maat N, DeCosmo J, Katsaros K B,Davidson K L, Bumke K, Hasse L, Chadwick H M. Sea surface wind stress and drag coefficients: the HEXOS results. Boundary-Layer Meteorology, 1992, 60: 109-142
[64] Drennan W M, Graber H C, Donelan M A. Evidence for the effects of swell and unsteady winds on marine wind stress. Journal of Physical Oceanography, 1999a, 29: 1853-1864
[65] Oost W A, Komen G J, Jacobs C M J, van Oort C. New evidence for a relation between wind stress and wave age from measurements during ASGAMAGE. Boundary-Layer Meteorology, 2002, 103: 409-438
[66] Fabrikant A L. Quasilinear theory of wind-wave generation. Izvestiya. Atmospheric and Oceanic Physics, 1976, 12: 524-526
[67] Janssen P A E M. Quasilinear approximation for the spectrum of wind-generated water waves. Journal of Fluid Mechanics, 1982, 117: 493-506
[68] Janssen P A E M. Wave-induced stress and the drag of air flow over sea waves. Journal of Physical Oceanography, 1989, 19: 745-754
[69] Makin V K, Kudryavstev V N, Mastenbroek C. Drag of the sea surface. Boundary-Layer Meteorology, 1995,73: 159-182
[70] Donelan M A, Drennan W M, Terray E A. Wave number spectra of wind waves in the range of 1-50 m. In: Banner, M.L. (Ed.), The Wind-Driven Air-Sea Interface. School of Mathematics, The University of New South Wales, Sydney, 1999: 35-42pp
[71] Tsimring L Sh. Induced scattering of surface wind waves. Izvestiya Atmospheric and Oceanic Physics, 1983, 19:47-50
[72] Johnson A K, Hojstrup J, Vested H J, Larsen S E. On the dependence of sea surface roughness on wind waves. Journal of Physical Oceanography, 1998, 28 (9): 1702-1716
[73] Lange B, Johnson H K, Larsen S, Hojstrup J, Kofoed-Hansen H, Yelland M J. On detection of a wave age dependency for the sea surface roughness. Journal of Physical Oceanography, 2004,34(6): 1441-1458
[74] Hwang P A. Temporal and spatial variation of the drag coefficient of a developing sea under steady wind-forcing. Journal of Geophysical Research, 2005, 110, C07024,doi: 10.1029/2005 JC002912.
[75] Kasilingam D P, O H Shemdin. The validity of the composite surface model and its application to the modulation of radar backscatter. International Journal of Remote Sensing, 1992, 13(11): 2079-2104
[76] Longuet-Higgins M S. The effect of nonlinearities on statistical distributions in the theory of sea waves. J. Fluid Mech., 1963, 17: 459-480
[77] BARBER N F. The directional resolving power of an array of wave detectors. In: Ocean wave spectra Prentice Hall, Englewood Cliffs, NJ, 1963: 137-250pp
[78] Long R B, and K Hasselmann. A variational technique for extracting directional spectra from multi-component wave data. Journal of Physical Oceanography, 1979, 9(2): 373-381pp
[79] J(?)hne B K, and K S Riemer. Two-dimensional wave number spectra of small-scale water surface waves. J. Geophys. Res., 1990, 95(11): 531-546
[80] Trokhimovski Y G, V G Irisov, E R Westwater, L S Fedor and V E Leuski. Microwave polarimetric measurements of the sea surface brightness temperature from a blimp during the Coastal Ocean Probing Experiment (COPE). Journal of Geophysical Research, 2000, 105(C3): 6501-6516
[81] Feindt F, Schr(?)ter J, Alpers W. Measurement of the ocean wave-radar modulation transfer function at 35 GHz from a sea-based platform in the North Sea. Journal of Geophysical Research, 1979, 91(C8): 9701-9708
[82] Keller W C and W J. Plant Cross sections and modulation transfer functions at L-Band Ku-Bands measured during the TOWARD experiment．J．Geophys．Res．，1990： 95(C9)16277～16289
[83]Hara T，E J Bock and D．Lyzenga．In situ measurements of capillary-gravity wave spectra using a scanning slope gauge and microwave radars．J．Geophys．Res，1994，99：12593～12602
[84]丁赟．风浪状态对海面风应力的影响[硕士学位论文]．青岛：中国海洋大学，2005
[85]吕红民，许金山．大型风浪水槽风浪统计特征的测量和分析．青岛海洋大学学报(自然科学版)，1996，26(4)： 431～438
[86]吕红民，曹露洁，许金山．大型风浪水槽风速分布的测量和分析．青岛海洋大学学报自然科学版，1996，26(1)： 17～23
[87]Kolmogorov A N．Dissipation of energy in a locally isotropic turbulence．Doklady Akad．Nauk．SSSR，1941，32： 141
[88]Taylor G I．The spectrum of turbulence，Proceedings Royal Society London，Series A，1938，164：476～490
[89]Edson J B，C W Fairall，P G Mestayer and S E Larsen．A study of the inertial-dissipation method for computing air-sea fluxes．J．Geophys．Res．，1991，96：10689～10711
[90]Large W G and Pond S．Open ocean momentum flux measurements in moderate to strong winds．J．Phys．Oceanogr．，1981，11：324～336
[91]Fairall C W，J B Edson，S E Larsen and P G Mestayer．Inertial-dissipation air-sea flux measurements： A prototype system using real time spectral computations．J．Atmos．Oceanic Technol．，1990，7： 425～453
[92]文圣常，宇宙文．海浪原理与计算原理．北京：科学出报社，1984
[93]徐德伦，余定勇．随机海浪理论．北京：高等教育出版社，2001
[94]张立振．快速滤波本征模态信号分解及其在海洋数据分析中的应用[博士学位论文]．青岛：中国海洋大学，2006
[95]Cooley and Tukey．An Algorithm for the Machine Calculation of Comples Fourier series． Mathematics of Computation, 1965, 19(90)
[96] Cooley J W, Lewis PAW and Welch P D. The fast Fourier transform and its application. IEEE transactions on education, 1969, 12(1)
[97] Littlewood J E and R E A C Paley. Theorems on Fourier series and power series. J. London Math. Soc, 1931,6:230-233
[98] Calder(?)n A P and Zygmund A. On the existence of certain singular integrals. Acta. Math., 1952,88:85-139
[99] Stein E M. Singular integrals and differentiability properties of functions. N. J. : Princeton Univ. Press., 1970
[100] STEIN WEISS. Introduction to Fourier Analysis on Euclidean Spaces. N. J.: Princeton Univ. Press., 1971
[101] Coifman R. A real variables characterization of H p. Studia Math., 1974, 51: 269-274
[102] Coifman R R. A real variable characterization of Hp. Studia Math., 1974, 51: 547-598
[103] Latter R. A decomposition of Hp (Rn) in term of atoms. Studia Math., 1977, 62: 92-101
[104] Calderon A P. An atomic decomposition of distributions in parabolic H spaces. Adv. in math., 1977,25:216-225
[105] Peetre J. New thought on Besov spaces. Duke Univ. Math., Series, 1976
[106] Battle G et al.. A phase cell cluster expansion for Euclidian field theories. Ann. of Physics., 1982,142:95-1391
[107] Meyer Y. Principed incertitude. Bases hilbertinnes et al gebra d'operataur. Seminaire Bourbaki, 1985-1986
[108] Lemarie P and Meyer Y. On delete set bases Hilhertiennes. Revista. Mathmatica. Ibero. American A., 1986,2(1): 1-18
[109] Daubechies. The Wavelet transform: Time-Frquency Localizaion and Signal Analysis. IEEE Trans, On Information Theory, 1990, 36(5)
[110] 崔锦泰著[美].小波分析导论.西安交通大学出版社,1995
[111]Huang N E，Long S R and Shen Z．The mechanism for frequency downshift in nonlinear wave evolution．Adv．Appl．Mech．，1996，32： 59～111
[112]Huang N E，Shen Z，Long S R，Wu M C，Shih H H，Zheng Q，Yen N C，Tung C C and Liu H H．The empirical mode decomposition method and the Hilbert spectrum for nonlinear and non-stationary time series analysis．Proc．R Soc．Land．A．，1998，454： 903～995
[113]Huang N E，Shen Z and Long S R．A new view of nonlinear water waves： the Hilbert spectrum．A．Rev．Fluid Mech．，1999，31：417～457
[114]Huang N E，Wu M C，Long S R，Shen S S，P Qu，W Gloersen P and Fan K L．A confidence limit for the empirical mode decomposition and Hilbert spectra analysis，Proc．R．Soc．Land A．，2003，459： 2317～2345
[115]徐德伦．海洋随机数据分析[中国海洋大学研究生讲义]．2006
[116]Alpers W and I Hennings．A Theory of the Imaging Mechanism of Underwater Bottom Topography by Real and Synthetic Aperture Radar．J．Geophys．Res．，1984，89(C6)：10529～10546
[117]Plant W J．A Relationship Between Wind Stress and Wave Slope．J．Geophys．Res．，1982，87： 1961～1967