Thermodynamics/Dynamics Coupling in Weakly Compressible Turbulent Stratified Fluids
Thermodynamics/Dynamics Coupling in Weakly Compressible Turbulent Stratified Fluids
复制标题
弱可压缩湍流分层流体中的热力学/动力学耦合
DOI：
10.5402/2012/609701
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
R. Tailleux
中科院分区：
文献类型：
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作者：
R. Tailleux
在传统和地球物理流体动力学中，通常通过不可压缩的 Boussinesq 近似来描述低马赫数和较小相对密度变化的分层湍流流体流动。尽管这种近似通常被解释为将热力学与动力学解耦，但本文回顾了最近的结果并得出了新的结果，表明当保留非绝热效应和非线性状态方程时，现实实际上更加微妙和复杂。这样的分析确实揭示了：（1）与通常假设的情况相反，膨胀/收缩的可压缩功仍然与机械能转换具有相当的重要性； (2) 在 Boussinesq 流体中，可压缩效应以密度变化引起的重力势能变化的形式出现。这使得对于任意非线性状态方程构建不可压缩流体热力学的完全一致的描述成为可能； (3) 基于使用可用势能和势焓预算的严格方法可用于量化膨胀/收缩功？在稳定流和瞬态流中，这揭示了？主要受分子扩散效应控制，并充当重要的动能汇。
In traditional and geophysical fluid dynamics, it is common to describe stratified turbulent fluid flows with low Mach number and small relative density variations by means of the incompressible Boussinesq approximation. Although such an approximation is often interpreted as decoupling the thermodynamics from the dynamics, this paper reviews recent results and derive new ones that show that the reality is actually more subtle and complex when diabatic effects and a nonlinear equation of state are retained. Such an analysis reveals indeed: (1) that the compressible work of expansion/contraction remains of comparable importance as the mechanical energy conversions in contrast to what is usually assumed; (2) in a Boussinesq fluid, compressible effects occur in the guise of changes in gravitational potential energy due to density changes. This makes it possible to construct a fully consistent description of the thermodynamics of incompressible fluids for an arbitrary nonlinear equation of state; (3) rigorous methods based on using the available potential energy and potential enthalpy budgets can be used to quantify the work of expansion/contraction ? in steady and transient flows, which reveals that ? is predominantly controlled by molecular diffusive effects, and act as a significant sink of kinetic energy.