标题： 二维有限箱中涡量衰减中的交叉现象 显示英文标题

标题： A Cross-Over in the Enstrophy Decay in Two-Dimensional Turbulence in a Finite Box

摘要： 本文中对一个大但有限的箱体内二维衰减湍流的数值模拟揭示了涡量衰减的两种物理上不同的区域。 在初始阶段，由随机高斯初始条件产生的涡量按 t^{-γ}衰减，其中 gamma 约为 0.7-0.8。 之后，流动经历向由不同涡旋组成的气体或流体的转变。 同时，衰减指数的大小发生交叉，变为 gamma 约为 0.4。 推导出了总涡旋数 N(t) 与单个涡旋平均环量之间的精确关系。 提出了一种理论，预测 N(t) 与 t^{-ξ}成正比，且指数 gamma=2/5 和 xi=4/5。还讨论了在非常晚的时间可能发生的进一步交叉，即 gamma=1/3 和 xi=2/3 的可能性。 显示英文摘要

摘要： The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this paper uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy, generated by a random Gaussian initial condition, decays as t^{-gamma} with gamma approximately 0.7-0.8. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to gamma approximately 0.4. An exact relation for the total number of vortices, N(t), in terms of the mean circulation of an individual vortex is derived. A theory predicting that N(t) is proportional to t^{-xi} and the magnitudes of exponents gamma=2/5 and xi=4/5 is presented and the possibility of an additional very late-time cross-over to gamma=1/3 and xi=2/3 is also discussed.