拉格朗日平均Navier-Stokes- $α$方程的动力学模型
A Dynamic model for the Lagrangian Averaged Navier-Stokes-$α$ Equations
摘要：
发展了拉格朗日平均Navier-Stokes- $α$（LANS- $α$）方程的动力学程序，其中参数$α$在各向异性方向上的变化是由模拟本身所包含的数据以自洽的方式确定的。动力学模型最初在强迫和衰减各向同性湍流中进行测试，其中$α$在空间上是恒定的，但允许随时间变化。结果表明，采用动态LANS- $α$程序可以更精确地模拟各向同性均匀湍流。与使用固定$α$的LANS- $α$模拟相比，能谱和总动能衰减被更准确地捕获。为了评价动态LANS- $α$模型在各向异性湍流中的适用性，对槽道湍流进行了先验试验。发现参数$α$沿壁法线方向变化。在实心墙附近，长度尺度$α$取决于与墙的距离，且在墙处值消失。另一方面，在远离壁面的地方，湍流更加各向同性，$α$接近几乎恒定的值。此外，动态LANS- $α$模型准确地捕捉了近壁区亚网格尺度应力的行为。动态LANS- $α$模型有可能将LANS- $α$方程的适用性扩展到更复杂的各向异性流动。
英文摘要：
A dynamic procedure for the Lagrangian Averaged Navier-Stokes-$α$ (LANS-$α$) equations is developed where the variation in the parameter $α$ in the direction of anisotropy is determined in a self-consistent way from data contained in the simulation itself. The dynamic model is initially tested in forced and decaying isotropic turbulent flows where $α$ is constant in space but it is allowed to vary in time. It is observed that by using the dynamic LANS-$α$ procedure a more accurate simulation of the isotropic homogeneous turbulence is achieved. The energy spectra and the total kinetic energy decay are captured more accurately as compared with the LANS-$α$ simulations using a fixed $α$. In order to evaluate the applicability of the dynamic LANS-$α$ model in anisotropic turbulence, a priori test of a turbulent channel flow is performed. It is found that the parameter $α$ changes in the wall normal direction. Near a solid wall, the length scale $α$ is seen to depend on the distance from the wall with a vanishing value at the wall. On the other hand, away from the wall, where the turbulence is more isotropic, $α$ approaches an almost constant value. Furthermore, the behavior of the subgrid scale stresses in the near wall region is captured accurately by the dynamic LANS-$α$ model. The dynamic LANS-$α$ model has the potential to extend the applicability of the LANS-$α$ equations to more complicated anisotropic flows.
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