A data-driven method for modelling dissipation rates in stratified turbulence
A data-driven method for modelling dissipation rates in stratified turbulence
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DOI：
10.1017/jfm.2023.679
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发表时间：
2023-12
影响因子：
3.7
通讯作者：
Sam F. Lewin;S. M. de Bruyn Kops;Colm‐cille P. Caulfield;G. Portwood
中科院分区：
文献类型：
--
作者：
Sam F. Lewin;S. M. de Bruyn Kops;Colm‐cille P. Caulfield;G. Portwood
摘要本文提出了一种深度概率卷积神经网络（PCNN）模型，用于预测分层湍流中小尺度混合特性的局部值，即湍流动能和密度方差的耗散率，$\vareps $和$\chi$。PCNN的输入是速度和密度梯度的垂直列，其动机是通常可从海洋中的微结构剖面仪获得的数据。该架构的目的是使该模型能够捕捉分层湍流的几个特征，特别是依赖小尺度各向同性的浮力雷诺数$Re_B：=\vareps/（\nu N^2）$，其中$\nu$是运动粘度和$N$是背景浮力频率，适当的局部平均密度梯度和湍流强度之间的相关性和捕获的重要性的尾巴的概率分布函数的值的耗散。经验修改版本的常用的各向同性模型$\varepsilon$和$\chi$，只依赖于垂直导数的密度和速度的基础上提出的渐近制度$Re_B\ll 1$和$Re_B\gg 1$，并作为一个具有指导意义的基准与数据驱动的方法进行比较。当训练和测试的分层衰减湍流的模拟访问一系列的湍流制度（与不同的值$Re_B$），PCNN优于各向同性的假设显着为$Re_B$减少，并进一步证明了改进的拟合经验模型。PCNN的差分灵敏度分析便于与理论模型进行比较，并提供了对特征的物理解释，使其能够做出改进的预测。
Abstract We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $\varepsilon$ and $\chi$. Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $Re_b:=\varepsilon /(\nu N^2)$, where $\nu$ is the kinematic viscosity and $N$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $\varepsilon$ and $\chi$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $Re_b\ll 1$ and $Re_b\gg 1$, and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $Re_b$), the PCNN outperforms assumptions of isotropy significantly as $Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.