相似重整化群的Navier-Stokes哈密顿量
Navier-Stokes Hamiltonian for the Similarity Renormalization Group
摘要：
Navier-Stokes哈密顿量是从第一性原理导出的。它的Hamilton方程被证明是等价的连续性，Navier-Stokes，和能量守恒方程的可压缩粘性流体。比较了Euler和Navier-Stokes哈密顿量的推导，前者具有与Euler方程相同的动力学特性，但从一开始就去掉了纳维-斯托克斯方程的粘性项。这两个哈密顿算子在三维空间和一维时间上有相同的自由度：6个独立的标量势，但它们的动力学场必然是不同的，因为有耗散的理论不能平滑地映射到没有耗散的理论上。耗散流体的动力学坐标场是一个矢量场，它存储了所有流体粒子的初始位置。因此，这些似乎是研究流体粒子随时间的任意分离的自然坐标。引入了经典的相似重整化群，并推导了Navier-Stokes哈密顿量的流动方程。最后，通过耗散正则Poisson括号的伽利略代数讨论了非相对论粘性流体的对称性。
英文摘要：
The Navier-Stokes Hamiltonian is derived from first principles. Its Hamilton equations are shown to be equivalent to the continuity, Navier-Stokes, and energy conservation equations of a compressible viscous fluid. The derivations of the Euler and Navier-Stokes Hamiltonians are compared, with the former having identical dynamics to the Euler equation with the viscosity terms of the Navier-Stokes equation dropped from the beginning. The two Hamiltonians have the same number of degrees of freedom in three spatial and one temporal dimension: six independent scalar potentials, but their dynamical fields are necessarily different due to a theory with dissipation not mapping smoothly onto one without. The dynamical coordinate field of a dissipative fluid is a vector field that stores the initial position of all of its fluid particles. Thus these appear to be natural coordinates for studying arbitrary separations of fluid particles over time. The classical similarity renormalization group is introduced and the first steps are carried out deriving a flow equation for the Navier-Stokes Hamiltonian. Finally, the symmetries of a nonrelativistic viscous fluid are discussed through its galilean algebra with dissipative canonical Poisson brackets.
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