The irrotational progressive gravity waves propagating on uniform currents in Lagrangian analysis and experiments Part 2. Experimental verification

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 propagating 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 propagating 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 propagating direction of the progressive waves.