Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models
Identifying and quantifying nonconservative energy production/destruction terms in hydrostatic Boussinesq primitive equation models
复制标题
识别和量化静水布辛涅斯克原方程模型中的非保守能量产生/破坏项
DOI：
10.1016/j.ocemod.2010.05.003
复制
发表时间：
2010
期刊：
影响因子：
3.2
通讯作者：
R. Tailleux
中科院分区：
文献类型：
--
作者：
R. Tailleux
在海洋环流数值模式的局地总能量平衡方程中，热力学和动力学之间的物理不一致通常会引入非保守的产生/破坏项。这些项可能会在动量方程和热力学方程中分别引起不受欢迎的力和/或非绝热项，这可以解释在模拟的洋流和水团中观察到的一些误差。本文发展了一个理论框架来提供一种确定这种非保守项的实用方法，这是在OGCM早期版本中使用的一个相对简单的静力Boussinesq原始方程的背景下进行的，其中至少确定了四个主要的势非守恒的能量来源：(1)“悬挂”动能耗散项；(2)假定位势或守恒温度为守恒量；(3)Boussinesq近似与温度和盐度湍流混合的参数化的相互作用；(4)由于Boussinesq近似而产生的一些绝热可压缩效应。在实践中，OGCM也拥有虚假的数字能源源和汇，但这里没有明确提到它们。除(1)外，已确定的非保守能源源/汇不是符号确定的，允许在全球整合时可能广泛取消。然而，在当地，这些项可能与被认为发生在海洋中的实际能量转换项具有相同的量级。虽然这些非保守能量项对海洋的总体精度和物理真实性的实际影响很难确定，但一个重要的问题是，它们是否会影响瞬变模拟，以及与不同能量储存库的重大重组相关的向不同环流体制的过渡。对一些可能的改进方案进行了研究。由此发现，通过使用守恒温度而不是势温，项(2)可以实质上减少至少一个数量级。然而，使用滞弹性近似只会略微减少(4)项，而不会影响(1)、(2)和(3)项，这最初被认为是大大提高能源预算准确性的一种可能办法。
This paper seeks to illustrate the point that physical inconsistencies between thermodynamics and dynamics usually introduce nonconservative production/destruction terms in the local total energy balance equation in numerical ocean general circulation models (OGCMs). Such terms potentially give rise to undesirable forces and/or diabatic terms in the momentum and thermodynamic equations, respectively, which could explain some of the observed errors in simulated ocean currents and water masses. In this paper, a theoretical framework is developed to provide a practical method to determine such nonconservative terms, which is illustrated in the context of a relatively simple form of the hydrostatic Boussinesq primitive equation used in early versions of OGCMs, for which at least four main potential sources of energy nonconservation are identified; they arise from: (1) the “hanging” kinetic energy dissipation term; (2) assuming potential or conservative temperature to be a conservative quantity; (3) the interaction of the Boussinesq approximation with the parameterizations of turbulent mixing of temperature and salinity; (4) some adiabatic compressibility effects due to the Boussinesq approximation. In practice, OGCMs also possess spurious numerical energy sources and sinks, but they are not explicitly addressed here. Apart from (1), the identified nonconservative energy sources/sinks are not sign definite, allowing for possible widespread cancellation when integrated globally. Locally, however, these terms may be of the same order of magnitude as actual energy conversion terms thought to occur in the oceans. Although the actual impact of these nonconservative energy terms on the overall accuracy and physical realism of the oceans is difficult to ascertain, an important issue is whether they could impact on transient simulations, and on the transition toward different circulation regimes associated with a significant reorganization of the different energy reservoirs. Some possible solutions for improvement are examined. It is thus found that the term (2) can be substantially reduced by at least one order of magnitude by using conservative temperature instead of potential temperature. Using the anelastic approximation, however, which was initially thought as a possible way to greatly improve the accuracy of the energy budget, would only marginally reduce the term (4) with no impact on the terms (1), (2) and (3).