當上游河流夾帶大量粗顆粒土砂進入湖泊或水庫時，會在河川與水庫水位線之交界處形成三角洲，Lorenzo-Trueba et al. [2009]曾提出包含兩個移動邊界於單一坡度上發展之Gilbert三角洲之實驗與理論分析，Lai and Capart [2009]也曾指出異重流三角洲(Hyperpycnal delta)及Gilbert三角洲在單一坡度上具有自我相似(self similarity)之實驗與理論分析。然而，少有研究指出在雙坡度岩盤上發展之三角洲是否保有自我相似之特性。本研究以解析解及小尺度物理模型實驗定量地探討水上及水下底床坡度改變時對Gilbert三角洲形貌之影響，並追蹤三角洲上緣(topset)與水面線之交點(shoreline)、三角洲上緣與岩盤之交點(bedrock-alluvial transition)及三角洲坡趾(delta toe)隨時間之演化過程。實驗中我們精準地控制上游之輸砂量(Q_s)、輸水量(Q_w)、水上底床坡度(S_1)及水下底床坡度(S_2)以進行定量的實驗與理論分析。實驗中透過每五秒的間格攝影以記錄三角洲之發展過程，並以數位影像處理定量測量出三角洲之底床高程隨時間之變化。實驗結果顯示當Gilbert三角洲在雙坡度岩盤上發展時會呈現不對稱的效應存在，在增加上游岩盤坡度時會加快三角洲往上加積及往前堆積之速率，使三角洲之shoreline往前堆積且bedrock-alluvial transition會因為岩盤底床的限制而只能稍微地往上游移動。相對地，增加水下底床坡度時反而會限制三角洲topset的發展並抑止bedrock-alluvial transition往上游移動的範圍；shoreline則會往原點移動，使三角洲的foreset呈現一狹長形的形貌。

A Gilbert delta forms at the shoreline by homopycnal flows, of which the density of inflow and receiving basin is the same. A delta evolving over bedrock channel involves two internal moving boundaries. Lorenzo-Trueba et al. [2009] reported experimental and theoretical analysis of a Gilbert delta over bedrock with single basement slope. In the same year, Lai and Capart [2009] also reported experimental and theoretical analysis of both hyperpycnal and Gilbert deltas over a single basement slope, and revealed different similarities within deltas. However, few researches had addressed whether a Gilbert delta over dual-slope bedrock exist self-similarity. In this study, we derive a new analytical solution and use small-scale experiments to explore the morphodynamics of a Gilbert delta over dual-slope bedrock channel. In experiment, we control upstream sediment(Q_s)、inflow(Q_w)、subaerial slope(S_1) and subaqueous slope(S_2) for quantitatively analysis. We use time lapse photograph to record the delta evolution every five seconds and measure the change of delta elevation with time by digital image processing. Our result, show that there is an asymmetric effect when a Gilbert delta develops over a dual-slope bedrock. An increase of subaerial slope pushes the delta forward and upward, giving rise to forward migration of shoreline and suppressed headward migration of bedrock-alluvial transition. In contrast, an increase of subaqueous slope pushes down the delta, suppressing the headward migration of bedrock-alluvial transition and forward migration of shoreline.

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