摘要 前人已將或然率觀念和訊息熵的理論廣泛地應用於許多的問題上，在流體力學問題方面也成功的應用於渠流和管流上，然而對於其他紊流流場的應用卻尚未成熟。但實際上，自然環境中大多數的流場皆屬於紊流流場，譬如邊界層流、射流、尾流等，這些流場可以統稱為剪力流(Shear flows)。本研究便是應用訊息熵的理論於紊流剪力流的研究上，利用最大熵值的觀念來推導紊流剪力流的流速分佈，並將實驗結果與前人的理論研究及實驗結果做一比較，進而使用推導所得的流速分佈來研究紊流剪力流的其他物理特性，在邊界層流部分利用熵理論的流速分佈式，推導求得邊界層流的延散係數、位移厚度與動量厚度的熵理論公式；而關於射流方面則探討了平均稀釋率與熵參數之間的關係，至於尾流熵參數與阻力係數及雷諾數的關係也是本研究的討論重點。分析的結果顯示，熵參數會隨著流況的均勻與否而有所改變，亦即在紊流剪力流場中，熵參數與流況受剪應力影響的大小，息息相關。而本研究由實驗結果分析歸納出流場中熵參數的決定方式，使得最大熵理論之流速剖面可以應用於分析剪力流場的問題上。 Abstract The concept of entropy based on the probability theory has been successfully applied in the modeling the velocity distribution of channel flow and pipe flow. The velocity distribution derived by the entropy-maximization principle has advantages over the Prandtl-von Karman velocity distribution for the velocity close to the boundary. In this research, similar approaches are used for the velocity distribution of turbulent shear flows, which include boundary layer flow, jet flow and wake flow. The derived velocity profiles are compared with the experimental results and existing velocity distributions, and show good agreement. Based on the new velocity profile, formulas for the dispersion coefficient, momentum thickness and displacement thickness of boundary layer flow are developed. Also, the dilution rate of jet flow and drag coefficient of wake flow are calculated. The relationship between the entropy parameter and the flow parameters are discussed.
