二波共存之質量與能量傳輸

Abstract

本文以兩個單頻率波互相追趕及一單頻率波通過潛堤兩種方式產生波波共存之波場，藉由粒子影像量測系統(P.I.V.)搭配影像連結技巧，研究當空間中同時存在兩種頻率波時，其速度向量場之變化、水粒子運動軌跡等情形，並探討動位能、質量傳輸速度實驗值與理論值之間的關係。 由實驗分析結果可知，速度向量場在兩種單一頻率波共存時，水粒子前進速度較單一頻率波通過潛堤慢，且變化也較小。在平均動位能方面，由於兩波共存之實驗條件皆屬於弱非線性範圍，因此平均動能及位能的值與理論值相當接近，但是以1Hz波通過潛堤產生二波共存的例子來看，由於較明顯的非線性作用，使得平均動能較大於平均位能。在質量傳輸速度方面，實驗值皆為接近零的負值，但理論值皆為正值，可能由於水體因非線性影響使向後退水時間較長，因此造成負值的情況產生。而最後能通量部分，在兩波共存的情況下，實驗結果顯示兩者皆會互相轉移能量，當入射波振幅越接近時，其能通量轉換也會較大。

Interactions between two sinusoidal waves were investigated in this thesis. The wave fields were generated by two different ways. One is a 2 Hz wave chased by a 1 Hz wave. The other one is generated by a 1 Hz wave propagating over a submerged rectangular step. A PIV measurement system was used to measure wave fields. The wave forms, velocity field and particle trajectories of wave fields were measured. The kinetic and potential energies of the two-wave propagation were calculated and compared with the theoretical values. Also, the averaged mass transport speeds were calculated. From the experimental results, it showed that the particle velocity of two travelling sinusoidal waves, is slower than the particle velocity generated by a wave passing through the submerged obstacle. The two travelling sinusoidal waves were generated both in weakly non-linear range. Therefore, their potential and kinematic energy are similar and very close to the values predicted by linear theory. However, the kinematic energy of the wave passing through a submerged obstacle is larger than its potential energy. Due to the existence of tank end, the mean mass transport velocity is negative but nearly zero. Finally, it was observed that there exists energy transfer between two waves in space. The most apparent transfer effect occurs when the amplitudes of two waves are nearly equal.