Traveling phenomena are prevalent in a variety of fields, from atmospheric science to seismography and oceanography. However, there are two main shortcomings in the current literature: the lack of realistic modeling tools and the prohibitive computational costs for grid resolutions useful for data applications. We propose a flexible simulation method for traveling phenomena. To our knowledge, ours is the first method that is able to simulate extensions of the classical frozen field, which only involves one deterministic velocity, to a combination of velocities with random components, either in translation, rotation or both, as well as to velocity fields point-wise varying with space and time. We study extensions of the frozen field by relaxing constraints on its spectrum as well, giving rise to still stationary but more realistic traveling phenomena. Moreover, our proposed method is characterized by a lower computational complexity than the one required for circulant embedding, one of the most commonly employed simulation methods for Gaussian random fields, in $\mathbb{R}^{2+1}$.

翻译：行进现象广泛存在于大气科学、地震学、海洋学等多个领域。然而现有文献存在两大不足：缺乏逼真的建模工具，且适用于数据应用的网格分辨率计算成本过高。本文提出一种灵活的行进现象模拟方法。据我们所知，这是首个能够模拟经典冻结场扩展形式的方法。经典冻结场仅包含单一确定性速度，而本方法可扩展至含随机分量的速度组合（无论是平动、旋转分量还是两者兼具），以及随空间和时间逐点变化的速度场。我们还通过放宽对冻结场谱的约束研究其扩展形式，从而产生仍保持平稳但更真实的行进现象。此外，本文方法的计算复杂度低于循环嵌入法——该方法是$\mathbb{R}^{2+1}$中高斯随机域最常用的模拟方法之一。