论文标题
时空湍流式随机场的流动
Flow of Spatiotemporal Turbulentlike Random Fields
论文作者
论文摘要
我们研究了统计上各向同性，均质和固定差异的拉格朗日轨迹。我们设计了这个偏流的欧拉速度场，以使其在时空和时间上变得渐近且多重分子，因为无限雷诺数在无限的雷诺数中的湍流现象学需要它。然后，我们为该字段的可区分版本以数值求解流程方程。我们观察到轨迹也变得粗糙，其特征是与我们规定的前进领域之一的赫斯特指数几乎相同。此外，即使考虑了分数高斯领域对流的最简单情况，我们在拉格朗日框架中证明了其他间歇性的校正。目前的方法涉及正确定义的随机领域，并要求进行严格的治疗方法，以解释我们的数字发现并加深我们对这个持久问题的理解。
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and multifractal, both in space and time, as it is demanded by the phenomenology of turbulence at infinite Reynolds numbers. We then solve numerically the flow equations for a differentiable version of this field. We observe that trajectories get also rough, characterized by nearly the same Hurst exponent as the one of our prescribed advecting field. Moreover, even when considering the simplest situation of the advection by a fractional Gaussian field, we evidence in the Lagrangian framework additional intermittent corrections. The present approach involves properly defined random fields, and asks for a rigorous treatment that would explain our numerical findings and deepen our understanding of this long lasting problem.
