Instability of Mud Flow through Irregular Channel

近年來在台灣土石流災害發生頻繁，但土石流的防制與預警卻一直都是很困難的部份，其中一個原因就是沒有人知道土石流是如何成長的，這也是為什麼需要去研究的土石流流動中的穩定性問題，並期望透過線性不穩定性分析(Linear Instability Analysis)這套古典的流體力學分析方式去研究更多有關土石流方面的基礎特性。在一般的土石流災害中可將其分類為礫石型土石流、泥流型土石流等，而在這些不同材料組成的土石流中，本文從中選擇泥流型土石流去探討，並使用賓漢流體(Bingham fluid)之本構關係式去近似。 在本文中首先假想泥流型土石流流經一矩形渠道，並從渠道中之基本流況，穩態均勻流(Steady-Uniform Flow)開始分析。爾後給予渠道邊壁和渠道底床一微小之擾動變化，利用微擾法將微小之擾動加入流況之控制方程式與邊界條件中，最後再針對流況的擾動解加以研究分析，討論是否擾動會隨著時間或空間而成長或消減，並以此作為判斷流況隨時間或空間是否穩定。 從所定義的標準流況中可發現，此種流況是隨著時間無條件性的不穩定，而流況不穩定的程度則受制於擾動的波長，長波的情況會相對於短波時穩定。另外在相同的慣性力作用下，發現降伏應力越小的流體或是外在重力效應越強時，都會導致流況越不穩定。若是有外在擾動如底床擾動或河岸擾動介入時，流況其自身的擾動波長與底床擾動波長或河岸擾動波長必須相同時，才會使得流況變得越來越不穩定，且寬渠道中底床的擾動會相對於河岸的擾動重要，反之在窄渠道中則是河岸擾動會相對於底床擾動重要。Debris flow is a major disaster in Taiwan. Nevertheless, the mitigation and prediction of debris flow disaster are still not technically achievable. One of the reason is a lack of information on the growth of debris flow. Therefore, we expected to find the growth of any small disturbance of debris flows by classic instability analysis. However, there is more constitutive laws to describe different debris fluids. We chose the mud fluids to research and used Bingham fluids model. In this study, we try to analyze instability problem in mud flows through the channel with disturbance on side bank and bed. For these objectives to be achieved, the article is structured as follows. We first solve the steady uniform flow analytically in rectangular channel, then invoked a small perturbation on the channel’s boundaries. Through the linear instability analysis, we study the flow condition from stable to unstable. Results show that the flow condition is determined unconditional unstable with time. The long wave motion is more stable than short wave, and the flow tend to be more and more unstable for the larger gravity effect or the lower yield stress. In the spatial instability, there is more unstable since the flow’s wavelength is the same as forcing wavelength. The bed forcing is more important than side bank in wide channel, otherwise the side bank forcing is more important in narrow channel