Two-way wave–vortex interactions in a Lagrangian-mean shallow water model
Two-way wave–vortex interactions in a Lagrangian-mean shallow water model
复制标题
拉格朗日平均浅水模型中的双向波与涡相互作用
DOI：
10.1017/jfm.2022.889
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发表时间：
2023
影响因子：
3.7
通讯作者：
Bühler, Oliver
中科院分区：
文献类型：
--
作者：
Maitland-Davies, Cai;Bühler, Oliver
我们推导并研究了涉及非色散波的波涡相互作用的简化模型，我们在二维浅水系统中研究该模型，着眼于在大气-海洋流体动力学中的应用。该模型由一组耦合的非线性偏微分方程组组成，用于拉格朗日平均速度和广义拉格朗日平均理论中定义的与波浪相关的赝动量矢量场。它允许波浪和由拉格朗日平均位涡分布控制的平衡流之间的双向相互作用，并且对于强解，它具有理想的波浪能和平均流能之和的精确能量守恒定律。我们的模型超越了标准光线追踪，因为我们可以使用弱双曲系统理论推导出包含赝动量场不连续性的弱解。这允许在不预测无限波幅的情况下形成焦散，就像标准光线追踪理论中的情况一样。适当的波力和耗散项被添加到模型中，并且模型的数值方案被实现为一组耦合的伪谱和有限体积积分器。给出了波包和简单涡旋结构之间相互作用的理想化示例来说明模型动力学。非受迫和非耗散模拟提出了“贪婪”波的启发式规则，即从长远来看，波场总是从平均流中提取能量。
We derive and investigate numerically a reduced model for wave–vortex interactions involving non-dispersive waves, which we study in a two-dimensional shallow water system with an eye towards applications in atmosphere–ocean fluid dynamics. The model consists of a coupled set of nonlinear partial differential equations for the Lagrangian-mean velocity and the wave-related pseudomomentum vector field defined in generalized Lagrangian-mean theory. It allows for two-way interactions between the waves and the balanced flow that is controlled by the distribution of Lagrangian-mean potential vorticity, and for strong solutions it features a desirable exact energy conservation law for the sum of wave energy and mean flow energy. Our model goes beyond standard ray tracing as we can derive weak solutions that contain discontinuities in the pseudomomentum field, using the theory of weakly hyperbolic systems. This allows caustics to form without predicting infinite wave amplitudes, as would be the case in the standard ray-tracing theory. Suitable wave forcing and dissipation terms are added to the model and a numerical scheme for the model is implemented as a coupled set of pseudo-spectral and finite-volume integrators. Idealized examples of interactions between wavepackets and simple vortex structures are presented to illustrate the model dynamics. The unforced and non-dissipative simulations suggest a heuristic rule of ‘greedy’ waves, i.e. in the long run the wave field always extracts energy from the mean flow.
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影响因子：
3.7
作者：
Jin-Han Xie;J. Vanneste
通讯作者：
Jin-Han Xie;J. Vanneste
影响因子：
3.7
作者：
Eric Danioux;J. Vanneste;O. Bühler
通讯作者：
Eric Danioux;J. Vanneste;O. Bühler
DOI：
10.1175/2007jas2561.1
发表时间：
2008-09
期刊：
--
影响因子：
--
作者：
A. Hasha
通讯作者：
A. Hasha
影响因子：
3.7
作者：
G. Wagner;W. Young
通讯作者：
W. Young
影响因子：
3.7
作者：
N. Pizzo;R. Salmon
通讯作者：
R. Salmon