论文标题
施用亚riemannian的几何形状应用于不可压缩的无粘液流体
Sub-Riemannian geometry applied to incompressible, inviscid fluids
论文作者
论文摘要
一个流体动力学领域涉及寻找各种原理。到目前为止，已经应用了汉密尔顿的视图和riemannian几何形状来找到用于流体动力学系统的大地测量学。与Riemannian几何形状相比，可以应用于搜索约束系统（例如涡流流）的地球化学，其中涡流运动受到与涡旋相关的保护法表示的旋转的限制。不可压缩的，无粘性流体动力学的NAMBU公式为两维流体（称为涡流 - 居民代数代数）提供了一个nilpotent Lie代数，这使得施加亚riemannian几何形状是自然的。作为第一种方法，我们考虑了离散的模型。用于二维不可压缩的无粘性离散点涡流的涡流测量学是已知的特殊点涡流星座，即平衡。我们还概述了3D涡流测量学的推导概念。
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian geometry can be applied to search for geodesics of constrained systems such as vortex flows, where the vortex motion is restricted by rotations that are expressed by vortex-related conservation laws. The Nambu formulation of incompressible, inviscid fluid dynamics provides a nilpotent Lie algebra for two- and three-dimensional fluids, called Vortex-Heisenberg algebra, which makes it natural to apply sub-Riemannian geometry. As a first approach we consider discretized models. The resulting vortex geodesics for two-dimensional incompressible, inviscid discrete point vortices is a known special point vortex constellation, the equilibrium. We also outline a concept for the derivation of 3D vortex geodesics.
