Comparison of two definitions of Lagrangian coherent structures in fluid flows and their numerical implementations

在二維流體流動中被動染劑的混合與相干結構的存在有著密切的關聯。至今還沒有關於它們的確切定義，我們將以圖形來呈現它的結構，統稱它們為拉格朗日相干結構。 在二維紊流中，我們介紹兩個定義的拉格朗日相干結構。一個是雙曲時間法(HTA)，另一個是有限時間Lyapunov指數(FTLE)。拉格朗日相干結構被定義為物質線，這些物質線比它們的周遭有著更長的穩定或不穩定時間。這樣的物質線代表著被動染劑在混合中之拉伸與摺疊。因此，我們可以藉由找到這些結構來瞭解混合效應較強的位置。 最後，在二維暫態流中，我們比較這兩種方法，並以圖例說明其結果。The mixing of passive tracers in two-dimensional fluid flows is intimately linked to the presence of coherent structures. Without being specific about their definition for now, we shall picture these structures, and refer to them as Lagrangian coherent structures. We introduce two definitions of Lagrangian coherent structures in two-dimensional turbulence. The first definition is Hyperbolic Time Approach(HTA), the second is Finite-Time Lyapunov Exponents(FTLE). The Lagrangian coherent structures are defined as material lines that are stable or unstable for longer times than any of their neighbors. Such material lines are responsible for stretching and folding in the mixing of passive tracers. Therefore, we can find these structures to know mixing effect is stronger than nearby trajectorys. Finally, we compare two approaches and illustrate the results on 2-D unsteady flows