有限水深水波Fermi-Pasta-Ulam递推的数值研究
Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth
摘要：
本文对重力场$g$中二维定深$h$上理想不可压缩流体的自由表面势流进行了高精度的直接数值模拟。在每个数值试验中，在$t=0$处，自由表面剖面的形式为$y=A_0\cos(2πx/L)$，速度场为${\bf v}=0$。计算结果表明，当初始波振幅$A_0\lesssim 0.12 h$和空间周期至少为$L\lesssim 120 h$时，系统发生Fermi-Pasta-Ulam（FPU）复发现象.复发时间$T_{\rm FPU}$与公式$T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$拟合良好。
英文摘要：
Highly accurate direct numerical simulations have been performed for two-dimensional free-surface potential flows of an ideal incompressible fluid over a constant depth $h$, in the gravity field $g$. In each numerical experiment, at $t=0$ the free surface profile was in the form $y=A_0\cos(2πx/L)$, and the velocity field ${\bf v}=0$. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes $A_0\lesssim 0.12 h$ and spatial periods at least $L\lesssim 120 h$. The time of recurrence $T_{\rm FPU}$ is well fitted by the formula $T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$.
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