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arXiv 2006.05707physics.flu-dynphysics.geo-ph
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热海洋中随机中尺度环流动力学

Stochastic mesoscale circulation dynamics in the thermal ocean

Darryl D. Holm, Erwin Luesink, Wei Pan

摘要:

与绝热可压缩流体动力学中的类似效应类似,浮力梯度对不可压缩分层流的影响被认为是“热”的。热旋转浅水(TRSW)模型方程包含三个小的无量纲参数。它们是Rossby数、Froude数和浮力参数。在这三个小参数的TRSW模型方程的渐近膨胀导致确定性的热版本的鲑鱼的L1(TL 1)模型和热准地转(TQG)模型,在扩大附近的热准地转平衡之间的流速和梯度的自由表面海拔和浮力。高波数时TQG的线性不稳定性倾向于在小尺度上产生环流。这种高波数不稳定性在许多计算模拟中可能是不可分辨的,但它在小尺度上的存在可能对可分辨尺度上的流体输运有显著贡献。有时,这种效应是通过“动能的随机反向散射”来模拟的。在这里,我们尝试另一种方法。也就是说,我们在模型TRSW/TL 1/TQG的层次结构中模拟“随机运输”。该模型是通过随机平流Lie运输(SALT)的方法,从最近推出的随机版本的欧拉-庞加莱变分原理。我们还指出了潜在的下一步应用这些模型的不确定性量化和数据同化的快速,高波数的影响,浮力前在这三个层次的描述,通过使用数据驱动的随机参数化算法,以前使用的SALT方法。

英文摘要:

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be `thermal'. The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon's L1 (TL1) model and the thermal quasi-geostrophic (TQG) model, upon expanding in the neighbourhood of thermal quasi-geostrophic balance among the flow velocity and the gradients of free surface elevation and buoyancy. The linear instability of TQG at high wave number tends to create circulation at small scales. Such a high wave number instability could be unresolvable in many computational simulations, but its presence at small scales may contribute significantly to fluid transport at resolvable scales. Sometimes such effects are modelled via `stochastic backscatter of kinetic energy'. Here we try another approach. Namely, we model `stochastic transport' in the hierarchy of models TRSW/TL1/TQG. The models are derived via the approach of stochastic advection by Lie transport (SALT) as obtained from a recently introduced stochastic version of the Euler--Poincaré variational principle. We also indicate the potential next steps for applying these models in uncertainty quantification and data assimilation of the rapid, high wavenumber effects of buoyancy fronts at these three levels of description by using the data-driven stochastic parametrisation algorithms derived previously using the SALT approach.

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