双频驱动超晶格法拉第波图案的数值模拟
Numerical simulation of a two-frequency-driven superlattice Faraday-wave pattern
- Imperial College London（帝国理工学院）
- Universidad de Santiago de Chile（智利圣地亚哥大学）
- Abdullah Al Salem University（阿卜杜拉·萨勒姆大学）
- Hongik University（弘益大学）
- Université Paris-Saclay（巴黎萨克雷大学）
- The University of Tokyo（东京大学）
- Université PSL（巴黎文理研究大学）
- Sorbonne Université（索邦大学）
- Université Paris Cité（巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文采用直接数值模拟（DNS）方法，研究双频驱动法拉第波的SSS-I超晶格图案形成，发现两条不同初始条件的路径最终均收敛至该鲁棒图案，且其失稳后会演变为动态版本。
AI中文摘要：
本文通过对带自由表面的完整三维纳维-斯托克斯方程进行直接数值模拟（DNS），研究了Arbell与Fineberg（1998、2002）发现并命名为SSS-I的双频驱动法拉第波中超晶格图案的形成过程。在法拉第波 onset 振幅高出25%的条件下，两组具有不同准六边形初始条件的模拟呈现出截然不同的演化路径，但均在约250个驱动周期后最终形成了相同的超晶格图案；该区域无法通过弱非线性或粘性近似方法获得。该驻波图案包含多组斑块，随时间交替表现为峰与谷，由类似DNA链骨架的长结构连接。图案的斑块与骨架可通过空间傅里叶分解关联，其结合了六边形模式与空间及时间次谐波模式。其中一条过渡路径经过多个寿命较长的瞬态状态，包括不同的六边形图案和另一种超晶格图案；另一条路径仅经过不稳定、无序的状态。再经过100个周期后，该图案失稳，被动态版本的SSS-I取代，其中超晶格受调制并沿骨架方向漂移，同时保留基本形状。在大几何构型的实验中、从两种不同初始条件出发的数值模拟中，以及最小几何构型中，均收敛至SSS-I状态，证明了SSS-I图案的鲁棒性。
英文摘要：
The formation of a superlattice pattern in two-frequency-driven Faraday waves discovered and named SSS-I by Arbell & Fineberg (1998, 2002) is investigated by means of Direct Numerical Simulations (DNS) of the full three-dimensional Navier--Stokes equations with a free surface. Two simulations with distinct quasi-hexagonal initial conditions run at a forcing amplitude $25\%$ above the Faraday-wave onset followed quite different routes, but both led eventually to the same superlattice pattern after around 250 forcing periods. This regime is inaccessible to the approximations of weak nonlinearity or viscosity. The standing-wave pattern contain rows of patches, alternating in time between hills and lakes that are connected by a long skeleton resembing the backbone of DNA strands. The patches and skeleton of the pattern can be related to its spatial Fourier decomposition, which combines hexagonal modes with a spatially and temporally subharmonic mode. One of the transition routes passes through several fairly long-lived transients including different hexagonal patterns and another superlattice pattern; the other passes only through erratic and disordered states. After another 100 periods, the pattern became unstable and was succeeded by a dynamic version of SSS-I in which the superlattice is modulated and drifts in the direction of the backbone, while preserving its basic shape. Convergence to SSS-I states both experimentally in a large geometry and numerically from two different initial conditions and in a minimal geometry demonstrates the robustness of the SSS-I pattern.
