Efficient numerical methods for wave-action transport and scattering

波作用输运和散射的高效数值方法

• 批准号: EP/W007436/1
• 负责人: Jacques Vanneste
• 金额: $ 7.88万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW007436%2F1
• 关键词: Efficient; numerical; methods; wave; action

Waves propagating in the atmosphere and ocean need to be represented in the numerical models used for weather and climate prediction in order to capture the strong impact they have on the atmospheric and oceanic circulation, on the state of the sea surface, and on the transport of pollutants. This cannot be achieved directly, however, because the typical wavelengths are much shorter than the grid scales of even the highest resolution numerical models. A reduced mathematical model that averages over the short wavelengths offers a solution but poses a major computational challenge. It describes the distribution of wave-action density in an extended position-wavenumber phase space; hence, it requires solving a partial differential equation in up to 6 space-like dimensions. This is beyond the reach of traditional discretisation methods. This project aims at demonstrating the feasibility of an alternative approach, based on a dynamical low-rank approximation of the wave-action density. This approach expands the wave action as a sum of products of functions of a few variables, constructed on-the-fly to project the dynamics onto the space of low-rank functions while minimising an error. The project will formulate an algorithm based on low-rank approximation and splitting, implement two versions that use different combinations of grid-based and spectral discretisations, and test them against a ray-tracing algorithm (specifically designed to capture the dynamics of a few wavepackets) and against direct numerical simulations of the underlying fluid equations. The formulation and implementation will emphasise parallelisation and efficiency on supercomputers, with testing carried out on ARCHER2. The project primarily targets the modelling of internal waves, with a focus on the representation of their scattering by turbulence and of nonlinear wave-wave interactions. Applications to ocean surface waves will also be considered.

在大气和海洋中传播的波浪需要在用于天气和气候预测的数值模式中表现出来，以便捕捉它们对大气和海洋环流、海面状况以及污染物输送的强烈影响。然而，这不能直接实现，因为典型的波长比即使是最高分辨率数值模型的网格尺度短得多。一个简化的数学模型，在短波长的平均提供了一个解决方案，但提出了一个主要的计算挑战。描述了波作用密度在扩展的位置-波数相空间中的分布；因此，它需要在多达6个类空间维度上求解偏微分方程。这是传统的离散化方法无法达到的。该项目旨在展示一种基于波作用密度的动态低秩近似的替代方法的可行性。这种方法将波动作用扩展为几个变量函数的乘积和，实时构建以将动态投影到低秩函数的空间中，同时最小化误差。该项目将制定一种基于低秩近似和分裂的算法，实现两个版本，使用基于网格和光谱离散的不同组合，并针对光线追踪算法（专门用于捕获几个波包的动态）和底层流体方程的直接数值模拟进行测试。该方案的制定和实施将强调超级计算机的并行化和效率，并在ARCHER2上进行了测试。该项目主要针对内波的建模，重点是湍流散射和非线性波-波相互作用的表示。还将考虑对海洋表面波的应用。

项目成果

Computing Lagrangian means

计算拉格朗日均值

• DOI: 10.1017/jfm.2023.228
• 发表时间: 2023
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Kafiabad H

Inertia-gravity-wave diffusion by geostrophic turbulence: the impact of flow time dependence

地转湍流引起的惯性重力波扩散：流动时间依赖性的影响

• DOI: 10.1017/jfm.2023.83
• 发表时间: 2023
• 期刊: Journal of Fluid Mechanics
• 影响因子: 3.7
• 作者: Cox M