周期域上的纳维-斯托克斯方程
The Navier-Stokes equations in periodic domains
摘要：
在本技术说明中，我们建立了非定常不可压缩流体动力学的原始变量的设置在空间周期性域中是病态的，因为边界速度的规格太宽而无法回避时间依赖性和近似误差。作为例子，我们证明了平面上的Taylor-Green解存在Hadamard发散，立方体上的ABC流是不唯一的。在边界值上没有纠正预防措施的均匀湍流的直接数值模拟中，我们的断言有助于我们理解经验丰富的滋扰，如能量耗散的收敛速度慢，统计矩的波动，或时间平均流量的自发浪涌。特别是，涡动力学不描述奇异积分方程。
英文摘要：
In the present technical note, we establish that the setting of the primitive variables of the unsteady incompressible fluid dynamics is ill-formulated in spatially periodic domains as the specification of the boundary velocity is too broad to sidestep time-dependency and approximation errors. As an illustration, we show that the Taylor-Green solution in planes suffers from the Hadamard-divergence, and the ABC flow in cubes is non-unique. In direct numerical simulations of homogeneous turbulence with no corrective precautions on the boundary values, our assertion helps us understand the well-experienced nuisances, such as slow rates of convergence in energy dissipation, fluctuations in the statistics moments, or spontaneous surges in the time-averaged flow quantities. In particular, vorticity dynamics is not described by singular integral equations.
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