Turbulent channel flow in weighted Sobolev spaces using the anisotropic Lagrangian averaged Navier-Stokes (LANS-$alpha$) equations
Turbulent channel flow in weighted Sobolev spaces using the anisotropic Lagrangian averaged Navier-Stokes (LANS-$alpha$) equations
复制标题
使用各向异性拉格朗日平均纳维-斯托克斯 (LANS-$alpha$) 方程计算加权 Sobolev 空间中的湍流通道流
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
S. Shkoller
中科院分区：
文献类型：
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作者：
D. Coutand;S. Shkoller
模拟槽道湍流的平均特性一直是一个
流体动力学长期存在的问题。虽然大量的
已经提出了各向同性湍流的数学模型，
相对较少的，如果有的话，湍流模型在各向异性壁有界
制度，在整个
频道近日
各向异性拉格朗日平均Navier-Stokes方程（局域网-$alpha$）具有
在[7]和[5]中，
本文主要分析了
这个耦合系统的非线性偏微分方程的平均速度和协方差
张量在通道几何中。协方差沿着的消失
墙诱导某些退化椭圆算子到模型中，
需要加权Sobolev空间来研究。我们证明了当无滑动
边界条件是为平均速度规定的，即局域网-α
方程
具有唯一的全局弱解，并且随着时间的推移而收敛
无穷大到唯一的静态解。
定性性质的固定的解决方案也建立。
Modelling the mean characteristics of turbulent channel flow has been one
of the longstanding problems in fluid dynamics. While a great number of
mathematical models have been proposed for isotropic turbulence, there are
relatively few, if any, turbulence models in the anisotropic wall-bounded
regime which hold throughout the entire
channel. Recently, the
anisotropic Lagrangian averaged Navier-Stokes equations (LANS-$alpha$) have
been derived in [7] and [5].
This paper is devoted to the analysis of
this coupled system of nonlinear PDE for the mean velocity and covariance
tensor in the channel geometry. The vanishing of the covariance along the
walls induces certain degenerate elliptic operators into the model, which
require weighted Sobolev spaces to study. We prove that when the no-slip
boundary conditions are prescribed for the mean velocity, the LANS-$alpha$
equations
possess unique global weak solutions which converge as time tends to
infinity towards the unique stationary solutions.
Qualitative properties of the stationary solutions are also established.