发表机构
Schlumberger Cambridge Research（施乐伯剑桥研究）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出任意维数受迫不可压缩Navier-Stokes方程的精确周期解构造，以横向对流场为体积力，提供显式速度、压力和力，并用于研究零功约束下的涡量集中。
AI 中文摘要
无外力不可压缩Navier-Stokes方程的精确周期解要求对流场为纯梯度场，以便将其吸收到压力中。对于先前考虑的循环三角函数族，这仅在孤立相位分配下以及三维和四维中发生。我们证明，互补的受迫问题允许对每个相位向量和每个维数n>=3进行精确构造。对于一个n参数族的两项循环场，该场是无散的且是拉普拉斯特征函数，将对流场的横向部分U^0作为体积力，给出了受迫方程的闭式解；对于3 <= n <= 8，我们确定U^0对每个相位向量都是非零的，因此强迫永远不会是平凡的。该强迫不做净功，因此动能纯粹以粘性方式衰减，对雷诺数没有限制。因此，该构造可作为任意维数下的精确基准，其中速度、压力和体积力都是显式的。我们还使用相同的构造来研究零功约束下的涡量集中。解析的零功计算显示，在所检查的雷诺数范围内，峰值涡量放大增加，并证明明显的饱和可能是由于空间分辨率不足造成的。
英文摘要
Exact periodic solutions of the unforced incompressible Navier-Stokes equations require the convective field to be a pure gradient, absorbed into the pressure; for the cyclic trigonometric families studied previously this occurs only at isolated phases and, over the range so far classified, only at n = 3 and 4. The forced problem, we show, admits an exact construction for every phase vector and every n >= 3. For an n-parameter family of two-term cyclic fields, solenoidal and a Laplacian eigenfunction, the transverse part U^0 of its convective field serves as the body force, giving a closed-form solution with velocity, pressure and force explicit. We prove closed forms for the pressure and for both magnitudes, in every dimension and with no upper bound on n: the forcing is never trivial, and the L^2 magnitude of U^0 stands to that of the whole convective field in the constant ratio 2*sqrt(2)/3, whatever the dimension, phase or units. The forcing does no net work, so the kinetic energy decays purely viscously at arbitrary Reynolds number, giving an exact benchmark in any dimension. A numerical study of vorticity concentration at zero applied work uses it as a reference, and shows that apparent saturation can be a resolution artefact.
Comments15 pages, 2 figures, 2 tables. Verification and solver scripts included as ancillary files
