無旋性前進重力波傳遞在均勻流中的Lagrangian解析解與試驗驗證Part 2.理論解析解

The Irrotational Progressive Gravity Waves Propagating on Uniform Currents in Lagrangian Analysis and Experiments. Part 2. Experimental Verification

陳陽益(Yang-Yih Chen) ； 林楚佑(Chu-Yu Lin) ； 李孟學(Meng-Syue Li) ； 李政達(Cheng-Ta Lee)

《海洋工程學刊》 12卷1期 (2012/06) Pp. 33-60

https://doi.org/10.6266/JCOE.2012.1201.02

摘要

針對Part 1（陳等，2012）的無旋性自由表面週期性規則前進重力波傳遞在均勻流中，本文以與前進波波向同向與反向的均勻流兩種特例情況，進行試驗量測所得的波形曲線、流速分佈、流體質點的運動軌跡與運動週期及其質量傳輸速率與Lagrangian平均高程等特性，皆與Part 1（陳等，2012）全以Lagrangian方式所得的三階解結果一致。本試驗證實，波流場中由同高程標註的流體質點運動所構成的波形曲線，其波長皆同於（純）前進波者，而其傳播速度為（純）前進波波速與均勻流流速之和是具Doppler效應的。再者，亦揭示出流體質點的運動軌跡的形狀，於前進波波向與均勻流同向中，依流體質點在波谷斷面處時沿前進波波向的流速分量為反向、零與正向時，則其形狀分別為朝波向前進的似扁長輻餘擺線、在波谷斷面處成尖點朝下的似滾輪線與似短輻餘擺線；而於前進波波向與均勻流反向中，當流體質點的質量傳輸速率為沿前進波波向為正向與零時，則其形狀分別為朝波向前進的縮短的似扁長輻餘擺線與長軸在前進波波向上似橢圓的封閉曲線，及當流體質點的質量傳輸速率為反前進波波向，但質點在波峰斷面處時沿前進波波向的流速分量分別為正向、零與反向時，則其形狀分別為反波向前進的似倒扁長輻餘擺線、在波峰斷面處成尖點朝上的似倒滾輪線與似倒短輻餘擺線。

關鍵字

試驗 ； 波形曲線 ； Doppler效應 ； 質點的軌跡形狀 ； 漂移速度 ； 運動週期 ； Lagrangian平均高程

並列摘要

The experiments are conducted to measure the motional characteristics of water particle motion for the progressive gravity waves interacting with following and reversing uniform currents. The theoretical results of the third-order Lagrangian solution in Part1show good agreements with the experimental data 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 positions of particles with same Lagrangian vertical label 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 particle orbits like the prolate trochiod, the cycloid and the curtate trochoid existing in the case of following uniform current as the horizontal velocity components of particles at the wave trough are, respectively, negative, zero and positive in the direction of the progressive waves. The orbits which 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. 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 wave crest are, respectively, positive, zero and negative in the direction of the progressive waves.

並列關鍵字

experiment ； wave-form ； Doppler effect ； particle's orbital form ； mass transport velocity ； particle's motion period and Lagrangian mean level