论文标题
Onsager湍流理论，约瑟夫森·安德森的关系和d'Alembert悖论
Onsager Theory of Turbulence, the Josephson-Anderson Relation, and the D'Alembert Paradox
论文作者
论文摘要
约瑟夫森·安德森（Josephson-Anderson）的关系，对描述固体周围流动的不可压缩的Navier-Stokes解决方案有效，即时将拖动消散的功率等同于D'Alembert所考虑的潜在Euler溶液的流动线的涡流通量。它的推导涉及将速度场分解为该背景电势段场和对应于人体后面旋转唤醒的电磁磁场，其中通量术语描述了从两个场之间的相互作用能量转移到旋转流的动能。我们建立了约瑟夫森·安德森（Josephson-Anderson）关系的有效性，该关系对以零粘度极限获得的欧拉方程的弱解，其有效性是由于粘性涡度通量而导致的一个转移项，而另一个由于粘性皮肤摩擦异常而引起的。此外，我们建立了相互作用和旋转能的局部平衡方程的弱形式。我们定义了这些能量的非线性空间通量，并表明相互作用能量与壁的渐近通量等于约瑟夫森·安德森（Josephson-Anderson）关系中的异常皮肤摩擦项。但是，当Euler溶液在墙壁处适当满足无流量的条件时，则异常的术语消失。在这种情况下，我们还可以表明，旋转能量的渐近通量必须消失，并且在旋转中获得粘液耗散异常和惯性耗散在旋转中唤醒了Onsager-Duchon-Robert的关系。通过这种方式，我们在约瑟夫森·安德森的关系与湍流理论之间建立了精确的联系，并提供了D'Alembert Paradox的新颖解决方案。
The Josephson-Anderson relation, valid for the incompressible Navier-Stokes solutions which describe flow around a solid body, instantaneously equates the power dissipated by drag to the flux of vorticity across the flow lines of the potential Euler solution considered by d'Alembert. Its derivation involves a decomposition of the velocity field into this background potential-flow field and a solenoidal field corresponding to the rotational wake behind the body, with the flux term describing transfer from the interaction energy between the two fields and into kinetic energy of the rotational flow. We establish the validity of the Josephson-Anderson relation for the weak solutions of the Euler equations obtained in the zero-viscosity limit, with one transfer term due to inviscid vorticity flux and the other due to a viscous skin-friction anomaly. Furthermore, we establish weak forms of the local balance equations for both interaction and rotational energies. We define nonlinear spatial fluxes of these energies and show that the asymptotic flux of interaction energy to the wall equals the anomalous skin-friction term in the Josephson-Anderson relation. However, when the Euler solution satisfies suitably the no-flow-through condition at the wall, then the anomalous term vanishes. In this case, we can show also that the asymptotic flux of rotational energy to the wall must vanish and we obtain in the rotational wake the Onsager-Duchon-Robert relation between viscous dissipation anomaly and inertial dissipation due to scale-cascade. In this way we establish a precise connection between the Josephson-Anderson relation and the Onsager theory of turbulence, and we provide a novel resolution of the d'Alembert paradox.
