| 摘要: | 潰壩顆粒流進入水體後所誘發之波浪現象，廣泛存在於自然災害與工程事件中，例如山崩入海、冰河塊崩落或工業堆料滑動等情境。其所造成之波浪動力不僅影響沿岸區域安全，也為近岸流體力學與流固耦合（Fluid-Solid Interaction）行為研究帶來挑戰。
本研究旨在探討顆粒柱崩塌入水過程中，不同初始縱橫比（Aspect Ratio）與體積分數（Solid Volume Fraction）對波浪生成機制之影響。透過實驗方法系統性地觀察與分析顆粒與水體間的動態交互，嘗試建立波浪行為與顆粒特性之間的量化關聯，並釐清其中之非線性響應特性。實驗設計採用可控顆粒柱模擬崩塌入水過程，使用粒徑均一的氧化鋁珠為主要材料，調整其初始縱橫比。另加入粒徑較小的石英砂填補間隙，以調整體積分數，觀察其對波浪產生與演化的影響。高頻攝影與影像處理技術被用以擷取顆粒速度場、水面輪廓變化與波浪幾何參數（浪高、波長、波速等）隨時間演化之資訊。數據分析涵蓋波浪與顆粒之時間尺度與空間尺度行為，並建立多組波浪參數與顆粒動能之間的函數關係。
實驗結果表明，波浪生成過程可歸納為三種典型模式：在顆粒柱高縱橫比條件下，波浪易形成激潮（bores），並因浪高過大而導致破碎；在中縱橫比條件下，則生成孤立波（solitary waves），可長時間穩定傳播且波形保持不變；而在低縱橫比條件下，則出現非線性過渡波（nonlinear transition waves），其波長分佈範圍較廣，且呈持續增長趨勢。顆粒前緣位置與速度的變化趨勢與波浪振幅呈高度相關，顯示顆粒動能為驅動波動的重要來源。其中，縱橫比為關鍵控制參數，高縱橫比條件下，顆粒柱擁有較高重力位能，入水動能集中釋放，產生更高的浪高與更快的波速；體積分數的提升有助於減少內部摩擦並增強流動協同性，進而促使波浪振幅與傳播距離呈現協同增長。然而，當縱橫比較低時，即使提高體積分數，波浪特徵參數反而呈現下降趨勢，顯示此類條件下顆粒柱運動受限，能量轉換效率不足。進一步分析顯示波浪特性呈現強烈非線性行為。高振幅波易誘發破波，並出現波速飽和現象；顆粒前緣則可能產生「推進—回退—沉積」的非穩態行為，顯示動量傳遞機制受到顆粒內部結構重組與反饋力影響。此外，本研究引用Robbe-Saule等人提出之局部福祿數經驗模型，其將最大無因次波幅與局部福祿數建立關係。根據實驗資料，本研究提出修正經驗關係式，於高縱橫比條件下表現良好，提升現有理論對於波浪振幅預測的適用性與準確性。
綜上所述，本研究成功揭示初始幾何與材料配置對顆粒潰塌入水波浪動力學之控制機制，並提出可供參考之經驗模型。成果可應用於潰壩模擬、海岸防災設計、流固耦合模型參數化等領域，亦為非線性波動與顆粒流互動研究提供實驗基礎與理論支持。
;Wave phenomena induced by granular dam-break flows entering a water body are common in both natural hazards and engineering scenarios, such as landslides into the sea, glacier calving, and industrial stockpile collapses. These wave dynamics not only affect coastal safety but also pose challenges to the study of nearshore hydrodynamics and fluid–solid interaction.
This study investigates the influence of initial aspect ratio and solid volume fraction on wave generation mechanisms during the collapse of a granular column into water. Laboratory experiments were conducted using monodisperse alumina beads to form granular columns with varying aspect ratios, while fine quartz sand was introduced to fill interstitial gaps and adjust the solid volume fraction. High-speed imaging and image processing techniques were employed to capture particle velocity fields, free-surface profiles, and temporal evolution of wave parameters (wave height, wavelength, wave speed). The collected data enabled quantitative analysis of the temporal–spatial scales of wave–particle interactions and the establishment of functional relationships between wave parameters and granular kinetic energy.
Results reveal three characteristic wave-generation regimes: (i) high aspect ratios produce bores prone to breaking due to excessive wave height; (ii) intermediate aspect ratios generate stable solitary waves that preserve their shape during long-distance propagation; and (iii) low aspect ratios result in nonlinear transition waves with broad and growing wavelength distributions. Wave amplitude correlates strongly with the position and velocity of the particle front, indicating granular kinetic energy as the primary driver. Aspect ratio was identified as the dominant control parameter: high aspect ratios yield greater gravitational potential energy, concentrated kinetic energy release, and consequently larger wave heights and faster wave speeds. Increasing solid volume fraction enhances internal flow coherence, promoting simultaneous growth of wave amplitude and propagation distance; however, for low aspect ratios, higher volume fractions led to reduced wave characteristics due to limited particle mobility and inefficient energy transfer. Nonlinear effects were evident—high-amplitude waves triggered breaking and wave-speed saturation, while particle fronts exhibited unsteady “advance–retreat–deposition” cycles driven by internal structural rearrangements and feedback forces.A modified empirical relationship, adapted from the local Froude number model of Robbe-Saule et al., is proposed to predict maximum nondimensional wave amplitude, demonstrating improved accuracy under high-aspect-ratio conditions.
Overall, this work elucidates the governing role of initial geometry and material configuration in the wave dynamics of granular dam-break flows, providing an experimental and theoretical basis for applications in dam-break modeling, coastal hazard mitigation, and parameterization of fluid–solid coupling models. |
