漸擴渠之單粒徑與多粒徑礫石砂丘形貌動力數值研究

Abstract

礫石砂丘之形態與輸砂行為，對河道阻力與河川形貌演變具有重要影響，而其演化機制更是理解礫石河床形貌動力之基礎問題。現有理論框架對其動力機制仍存在空缺，且在定義與分類上多以形態特徵為主，缺乏明確之動力判準。本研究團隊在新店溪上游山區漸擴礫石河段中，曾於颱洪事件前後觀察到舌狀砂丘之發育，然其演化過程仍缺乏充分了解。本研究旨在透過 Delft3D 進行二維深度平均之動床數值模擬，系統性探討礫石砂丘之形成與演化過程。研究透過三階段數值模擬逐步解析其動力機制：首先以單粒徑、現地同尺度之簡化漸擴渠道，解析礫石砂丘之基礎動力機制；其次納入多粒徑輸砂之篩化行為，探討複合動力下之砂丘演化；最後以完整條件進行現地模擬，以重現並解釋颱洪事件中砂丘之發展歷程。 單粒徑水槽共進行66組情境模擬，觀察到一致的形貌發展過程。床形由平床逐漸發展為砂丘，初期受渠道漸擴影響而產生他發性演化，渠寬漸擴使流速及剪應力遞減，形成淤積性床形，有別於定寬渠或漸縮渠所發展之床形。隨床形高度持續累積，砂丘轉為自發性演化，水理、輸砂與形貌之間產生持續交互作用，並形成一回饋循環機制。此循環由床面局部增積引致流場重分配，形成剪應力梯度及輸砂梯度，促進砂丘增積與推進，再回饋流場。本研究提出比流量差作為量化指標，發現迎風面出現局部水流兩側化，並於背風面重新集中時，將形成水深驟增並觸發回饋循環。據此，提出以水流兩側化作為砂丘在動力上存在之判定基準。 多粒徑水槽共進行78組模擬，在納入篩化行為後，觀察到篩化前緣與延長背風面之複合砂丘。本研究延續回饋循環機制之分析，說明篩化床面仍可產生具砂丘動力行為之形貌。結果顯示，剪應力梯度與粒徑梯度之權重關係具有高度相關性，並可據以區分砂丘頂點與篩化前緣之主導機制。基於上述機制，提出以粒徑為基礎之可動性指數作為動力分類參數，並與渠寬漸擴率共同作為礫石床形分類依據。模擬結果顯示，當漸擴率大於0.1且可動性指數大於0.65時，床面將具備產生砂丘回饋循環之能力。 現地颱洪事件之數值模擬結果顯示，中央砂洲頂部之舌狀砂丘亦呈現回饋循環之交互行為。比流量差與可動性指數之量化方式，經適當修正後可應用於現地複雜條件中。模擬結果指出，可動性指數隨流量變化跨越門檻時，床形將於複合砂丘與純礫石砂丘之間轉換，並可合理解釋退水過程中砂丘向平床之演化歷程。整體而言，本研究證實礫石砂丘之持續發展源於水流兩側化所啟動之回饋循環，並據此建立以水動力與形貌動力為基礎之礫石床形分類判準，統整水槽與現地觀測結果。

Gravel dune morphology and sediment transport behavior exert significant influences on channel bed resistance and river morphodynamics, and their evolution mechanisms constitute a fundamental problem in understanding the dynamics of gravel-bed morphology. However, existing theoretical frameworks still contain gaps in explaining the governing mechanisms, and current definitions and classification system rely primarily on morphological characteristics, lacking clear dynamic criteria. In the upstream mountainous reach of the upper Xindian River, we observed that a linguoid gravel dune formed during three consecutive flood events, yet their evolution processes remain poorly understood. This study aims to systematically investigate the formation and evolution of gravel dunes using the two-dimensional depth-averaged morphodynamic model Delft3D. A three-stage numerical approach was adopted to progressively resolve the governing mechanisms. First, schematized simulations with single-size gravel, field-scale gradually expanding channels were used to identify the fundamental dynamics of gravel dunes. Second, grain-sorting processes were included to examine dune evolution under composite mechanisms. Finally, simulations of the upper Xindian River field case were conducted to reproduce and interpret dune development during flood events. In the single-size numerical flume experiments, a total of 66 scenarios were simulated, revealing a consistent morphological evolution process. The bed feature evolved from an initial plane bed into a dune bedform. In the early stage, this evolution was allogenic, driven by the gradual expansion of the channel. The channel expansion reduced flow velocity and bed shear stress, resulting in a depositional feature distinct from those formed in constant-width or gradually constricting channels. As the dune continued to grow, the evolution transitioned to autogenic, governed by continuous interactions among hydraulics, sediment transport, and morphology. This process forms a feedback loop mechanism, in which local bed aggradation redistributes the flow field, generating gradients in bed shear stress and sediment transport, and subsequently promoting dune growth and migration. Specific discharge difference was introduced as a quantitative indicator of flow bifurcation. Results show that when the flow bifurcation occurs on the stoss side and re-concentration on the lee side, a local increase in water depth is induced, triggering the feedback loop. Based on this finding, flow bifurcation is proposed as a dynamic criterion for autogenic evolution of gravel dunes. In the multi-size numerical flume experiments comprising 78 scenarios of different grain sorting processes, shallow sorting fronts and complex dunes with extended lee sides were observed. By applying the feedback loop mechanism, the results demonstrate that multi-size gravel beds still exhibit dynamic dune behaviors. A strong correlation was found between shear-stress gradients and grain-size gradients, allowing the dominant mechanisms at the dune crest and sorting front to be distinguished. Based on these findings, a grain-size-based mobility index is proposed as a dynamic parameter for bedform classification, along with the rate of channel expansion to be used as a geometric parameter. Results show that when the expansion rate exceeds 0.1 and the mobility index exceeds 0.65, the feedback loop was established sustaining dune development. Simulations of field case further show that the linguoid dune that formed on the crest of the mid-channel bar during floods exhibit a similar feedback mechanism. Applications of the specific discharge difference and mobility-based classification, with appropriate modifications, were successful under complex real-world conditions. Results indicate that transformation would occur between simple and complex gravel dunes as the mobility index became above or below the threshold value with changing discharge, explaining the observed dune planed-down during the falling stage of flood events. Overall, this study demonstrates that gravel-dune development is sustained by a feedback loop initiated by flow bifurcation, and establishes a dynamics-based classification framework that unifies flume and field observations.