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The quantitative experiments are made to measure the motional characteristics of water particles in the progressive gravity waves propagating on following and reversing uniform currents. The theoretical results of the third-order Lagrangian solution in Part 1[1] are shown good agreements with those measured by the experiments for the wave-form, the velocity distribution, the mass transport velocity, the particle trajectory, particle's motion period and Lagrangian mean level. It is also verified that identifying parameters of each particle is equal to the coordinates of its position in a still water. Consequentially, the wavelengths of the wave-forms constituted by the particles in the field are all equal to that of the progressive waves and their propagating speeds are the sum of the velocities of the progressive waves and the uniform current as the so-called Doppler effect is proved, but the motion periods and the Lagrangian mean levels of particles are the same as those in the progressive waves. The variations of the orbital forms of particles in the field are also revealed that the orbits like the prolate trochiod, the cycloid and the curtate trochoid are presented in the case of following uniform current as the horizontal velocity components of particles at the section of wave trough are, respectively, negative, zero and positive in the direction of the progressive waves, and that the orbits like the prolate trochoid and the ellipse are occurred in the case of reversing uniform current as the mass transport velocities of particles are, respectively, positive and zero in the direction of the progressive waves, and that the orbits like the turned prolate trochoid, the turned cycloid and the turned curtate trochiod are appeared in the case of reversing uniform current when the mass transport velocities of particles are negative and the horizontal velocity components of particles at the section of wave crest are, respectively, positive, zero and negative in the direction of the progressive waves.
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Keywords:
- Doppler effect /
- particle's orbital and motion period /
- mass transport velocity /
- Lagrangian mean level
[1] Chen Y Y, Hsu H C, Chang H K 2012 Acta Phys. Sin. 61 034702(in Chinese)[陈阳益, 许弘莒, 张宪国 2011 61 034702]
[2] Longuet-Higgins M S, Stewart R W 1960 J. Fluid Mech. 8 565
[3] Longuet-Higgins M S, Stewart R W 1961 J. Fluid Mech. 10 529
[4] Jonsson I G, Skougaard C, Wang J D 1970 Proc. 12th Coastal Eng. Conf.(New York: ASCE)1 489
[5] Josson I G 1977 J. Hydrual. Res. 16(3)223
[6] Josson I G, Brink-Kjaer O, Thomas G P 1978 J. Fluid Mech. 87 401
[7] Peregrine D H 1976 Adv. Appl. Mech. 16 9
[8] Thomas G P 1981 J. Fluid Mech. 110 457
[9] Thomas G P 1990 J. Fluid Mech. 216 505
[10] Baddour R E, Song S W 1990 Ocean Engng. 17 551
[11] Chen Y Y, Juang W J 1990 Proceeding of the 12th Ocean Engineering Conference in Taiwan(Taiwan: The Taiwan Society of Ocean Engineering)p248(in Chinese)[陈阳益, 庄文杰 1990 第十二届海洋工程研讨会论文集(台湾: 台湾海洋工程学会)第248页]
[12] Chang H K, Chen Y Y 1993 Harbour Technology 8 24(in Chinese)[张宪国, 陈阳益 1993 港湾技术 8 24]
[13] Groeneweg J, Battjes J 2003 J. Fluid Mech. 478 325
[14] Musumeci R E, Cavallo L, Foti E, Scandura P 2006 J. G. R. 111 c07019
[15] Olabarrieta M, Medina P, Castanedo S 2010 Coastal Engineering 57 643
[16] Morison J R, Crookes R C 1953 Tech. Memo.(U.S.: Army Corps of Engineers, Beach Erosion Board)40
[17] Longuet-Higgins M S 1986 J. Fluid Mech. 173 683
[18] Chen Y Y, Lin S S, Ho L S 1998 Proceeding of the 20th Ocean Engineering Conference in Taiwan(Taiwan: The Taiwan Society of Ocean Engineering)p60(in Chinese)[陈阳益, 林受勋, 何良胜 1998 第二十届海洋工程研讨会论文集(台湾: 台湾海洋工程学会)第60页]
[19] Pullen J, Arnott A, Buick J M, Greated C 1998 Euro. Mech. 387
[20] Chen Y Y, Hsu H C, Chen G Y 2010 Fluid Dyn. Res. 42 1
[21] Davies A G, Heathershow A D 1984 J. Fluid Mech. 144 419
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[1] Chen Y Y, Hsu H C, Chang H K 2012 Acta Phys. Sin. 61 034702(in Chinese)[陈阳益, 许弘莒, 张宪国 2011 61 034702]
[2] Longuet-Higgins M S, Stewart R W 1960 J. Fluid Mech. 8 565
[3] Longuet-Higgins M S, Stewart R W 1961 J. Fluid Mech. 10 529
[4] Jonsson I G, Skougaard C, Wang J D 1970 Proc. 12th Coastal Eng. Conf.(New York: ASCE)1 489
[5] Josson I G 1977 J. Hydrual. Res. 16(3)223
[6] Josson I G, Brink-Kjaer O, Thomas G P 1978 J. Fluid Mech. 87 401
[7] Peregrine D H 1976 Adv. Appl. Mech. 16 9
[8] Thomas G P 1981 J. Fluid Mech. 110 457
[9] Thomas G P 1990 J. Fluid Mech. 216 505
[10] Baddour R E, Song S W 1990 Ocean Engng. 17 551
[11] Chen Y Y, Juang W J 1990 Proceeding of the 12th Ocean Engineering Conference in Taiwan(Taiwan: The Taiwan Society of Ocean Engineering)p248(in Chinese)[陈阳益, 庄文杰 1990 第十二届海洋工程研讨会论文集(台湾: 台湾海洋工程学会)第248页]
[12] Chang H K, Chen Y Y 1993 Harbour Technology 8 24(in Chinese)[张宪国, 陈阳益 1993 港湾技术 8 24]
[13] Groeneweg J, Battjes J 2003 J. Fluid Mech. 478 325
[14] Musumeci R E, Cavallo L, Foti E, Scandura P 2006 J. G. R. 111 c07019
[15] Olabarrieta M, Medina P, Castanedo S 2010 Coastal Engineering 57 643
[16] Morison J R, Crookes R C 1953 Tech. Memo.(U.S.: Army Corps of Engineers, Beach Erosion Board)40
[17] Longuet-Higgins M S 1986 J. Fluid Mech. 173 683
[18] Chen Y Y, Lin S S, Ho L S 1998 Proceeding of the 20th Ocean Engineering Conference in Taiwan(Taiwan: The Taiwan Society of Ocean Engineering)p60(in Chinese)[陈阳益, 林受勋, 何良胜 1998 第二十届海洋工程研讨会论文集(台湾: 台湾海洋工程学会)第60页]
[19] Pullen J, Arnott A, Buick J M, Greated C 1998 Euro. Mech. 387
[20] Chen Y Y, Hsu H C, Chen G Y 2010 Fluid Dyn. Res. 42 1
[21] Davies A G, Heathershow A D 1984 J. Fluid Mech. 144 419
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