本論文為快速乾燥顆粒流之零階封閉紊流流動模型，對紊流邊界層(TBL)和被動層(PL)進行探討。運用了熱力學第一、第二定律和Müller-Liu熵增原理得到平衡封閉關係，加上動力反應、紊流的亥姆霍茲自由能、材料黏度、紊流黏度、次塑性，建立出封閉模型，再加上邊界條件定義問題，適用於分析不可壓縮顆粒經由重力驅動平穩從斜坡上滑下的山崩，並與層流解作比較。
結果顯示，平均體積分率和平均速度的圖形曲線中，在斜坡平面是最小值，以指數形式往自由表面發展形成最大值，兩種紊流動能和消散圖形，則是以相反的趨勢呈現。兩種紊流動能和消散大多被限制在接近斜坡平面上薄的紊流邊界層內，而在被動層的紊流動能是趨近於零和有限的紊流消散。快速顆粒流中的紊流邊界層和被動層與牛頓流體在紊流邊界層的情形相似。

Characteristics of the turbulent boundary and passive layers of an isothermal dry granular avalanche with incompressible grains are studied by the proposed zero-order turbulence closure model. The established closure model is applied to analyses of a gravity-driven stationary avalanche with incompressible grains down an incline. While the volume fractions and mean velocity increase from their minimum values on the plane toward maximum values on the free surface exponentially, two-fold turbulent kinetic energies and dissipations evolve in reverse manner. Most two-fold turbulent kinetic energies and dissipations are confined within the thin turbulent boundary layer immediately above the plane, with nearly vanishing two-fold turbulent kinetic energies and finite two-fold turbulent dissipations in the passive layer. Two layers are similarity to those of Newtonian fluids in turbulent boundary layer flows, and are preferable recognized by the distributions of the turbulent kinetic energies and dissipations.

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