Mathematical Modelling of Nonlinear Ring Waves of Moderate Amplitude in Fluids

流体中中等幅度非线性环波的数学模型

• 批准号: 2458723
• 金额: --
• 依托单位: Loughborough University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2458723
• 关键词: Mathematical; Modelling; Nonlinear; Ring; Waves

Surface and internal waves in the oceans have a strong effect on offshore structures, underwater cables and submersibles. They also contribute to ocean mixing processes, which are important for climate. Internal waves generated in straits, river-sea interaction areas and by localised topographic features are nearly annular (ring-shaped) in form and often propagate over an underlying current. Our project aims to develop appropriate mathematical models and to use them to study the properties and behaviour of such and similar waves with an emphasis on waves of moderate amplitude.Recently, it was shown that despite the clashing geometries of the waves and the current, there exists a linear modal decomposition that is different from the known decomposition for plane waves [1]. This decomposition was used to describe analytically the distortion of the wavefronts of weakly-nonlinear surface and internal waves, and to systematically develop and use mathematical models in order to solve some applied problems [2, 3]. The proposed work will be devoted to developing new advanced models for the waves of moderate amplitude, and to using them in order to study the behaviour of both surface and internal waves for different types of stratification and currents, as well as developing our understanding of the two-dimensional aspects of stability of the ring waves. The research will employ a variety of analytical and numerical methods.References:[1] K.R. Khusnutdinova, X. Zhang, Long ring waves in a stratified fluid over a shear flow, J. Fluid Mech. 794 (2016) 17-44.[2] K.R. Khusnutdinova, X. Zhang, Nonlinear ring waves in a two-layer fluid, Physica D: Nonlinear Phenomena 333 (2016) 208-221.[3] K.R. Khusnutdinova, Long internal ring waves in a two-layer fluid with an upper-layer current, Russ. J. Earth Sci. 20 (2020) ES4006.

海洋中的表面波和内波对近海结构物、水下电缆和潜水器有很大的影响。它们还促进了海洋混合过程，这对气候很重要。在海峡、江海相互作用区和局部地形地貌产生的内波几乎是环形的(环状)，通常在底层洋流上传播。我们的项目旨在建立适当的数学模型，并利用它们来研究这种波和类似波的性质和行为，重点是中等幅度的波。最近的研究表明，尽管波和流的几何形状相互冲突，但存在不同于已知的平面波分解的线性模式分解。这种分解被用来解析地描述弱非线性表面波和内波的波前失真，并系统地发展和使用数学模型以解决一些应用问题[2，3]。拟议的工作将致力于发展中等幅度波的新的高级模式，并利用它们来研究不同类型的层结和海流的表面波和内波的行为，以及发展我们对环波稳定性的二维方面的理解。参考文献：[1]K.R.KHusnutdinova，X.Zhang，剪切流上分层流体中的长环形波，J.流体力学。794(2016)17-44.[2]K.R.KHusnutdinova，X.Zhang，两层流体中的非线性环波，Physica D：非线性现象333(2016)208-221.[3]K.R.KHusnutdinova，具有上层流的两层流体中的长内环波，Russ.J.地球科学。20(2020)ES4006。