Parameterization of two-dimensional turbulence using an anisotropic maximum entropy production principle
Parameterization of two-dimensional turbulence using an anisotropic maximum entropy production principle
复制标题
使用各向异性最大熵产生原理对二维湍流进行参数化
DOI：
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发表时间：
2003
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通讯作者：
F. Bouchet
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作者：
F. Bouchet
我们认为未解决的尺度的影响，二维和地球物理流的建模。我们首先表明，小尺度上的粗粒度的字段的效果，可以近似在领先的顺序，由应变张量的涡度梯度，这正好保持了能量的效果。我们表明，这种近似将导致不稳定的数值代码。为了提出一个稳定的参数化，同时考虑到这些动力学性质，我们应用最大熵产生原理。参数化作为一个选择性的扩散成比例的平均应变，在收缩方向上，同时保存的能量。数值计算表明，得到的\外语{法语}{各向异性松弛方程}给出了一个重要的可预测性的改善，相对于Navier-Stokes，Smagorinsky或超粘性参数化。
We consider the modeling of the effect of unresolved scales, for two-dimensional and geophysical flows. We first show that the effect of small scales on a coarse-grained field, can be approximated at leading order, by the effect of the strain tensor on the gradient of the vorticity, which exactly conserves the energy. We show that this approximation would lead to unstable numerical code. In order to propose a stable parameterization, while taking into account of these dynamical properties, we apply a maximum entropy production principle. The parameterization acts as a selective diffusion proportional to the mean strain, in the contraction direction, while conserving the energy. We show on numerical computation that the obtained \foreignlanguage{french}{anisotropic relaxation equations} give an important predictability improvement, with respect to Navier-Stokes, Smagorinsky or hyperviscous parameterizations.