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.

在天气和气候预测的数值模型中，需要在大气和海洋中传播的波浪表示，以捕获它们对大气和海洋循环的强烈影响，对海面状态以及污染物的运输。但是，这不能直接实现，因为典型的波长比最高分辨率数值模型的网格尺度要短得多。在短波长上平均的减少数学模型提供了解决方案，但构成了重大的计算挑战。它描述了在扩展位置波相空间中波动密度的分布；因此，它需要在多达6个空间样的尺寸中求解部分微分方程。这是传统离散方法无法实现的。该项目旨在基于波动密度的动态低级别近似，证明替代方法的可行性。这种方法将波动作用扩展为几个变量函数的产物之和，并直接构建，以将动力学投射到低级函数的空间，同时最小化误差。该项目将基于低级别近似和拆分制定算法，实施两个版本，使用不同的基于网格的基于网格和光谱离散的组合，并针对射线追踪算法进行测试（专门设计用于捕获几个Wavepackets的动态），并针对下部流体的直接数字模拟。配方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。该项目主要针对内部波的建模，重点是通过湍流和非线性波波相互作用来表示其散射。还将考虑到海面波的应用。

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