Abstract

The study of the development of perturbations under the influence of various hydrodynamic instabilities, as well as the transition to turbulent mixing and turbulence, has been a subject of considerable interest over the past decades. This is primarily due to the importance of these phenomena in various fields of science and engineering. In addition, it should be noted that studies of the characteristics of turbulent flows, for example, have still not been completed. This is inspiring a great deal of interest in this topic, both in the sense of physical theory and in the sense of developing new approaches to the mathematical modeling of the corresponding problems. The capabilities of modern computer technology make it possible to carry out numerical experiments in two-dimensional and three-dimensional setups and analyze the features of the new numerical methods. Presently, numerous methods with many modifications are used in practice. This review focuses on the most promising among them.

中文翻译：

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水动力不稳定性和湍流混合发展的现代数学建模方法

摘要

在过去的几十年中，对各种流体动力学不稳定性的影响以及向湍流混合和湍流过渡的扰动发展的研究一直是相当感兴趣的主题。这主要是由于这些现象在科学和工程学的各个领域中的重要性。另外，应该注意的是，例如，关于湍流特性的研究还没有完成。从物理理论的意义以及为相应问题的数学建模开发新方法的意义上，这激发了对该主题的极大兴趣。现代计算机技术的功能使在二维和三维设置中进行数值实验以及分析新数值方法的特征成为可能。当前，在实践中使用了具有许多修改的许多方法。这篇评论集中在其中最有希望的方面。