在对数格子上的可逆纳维埃-斯托克斯方程
Guillaume Costa1, Amaury Barral1, Bérengère Dubrulle1
1Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France.
Physical review. E
|July 19, 2023
概括
本研究使用高分辨率模拟来探索可逆纳维埃-斯托克斯 (RNS) 方程. 我们发现了二次阶段过渡,证实了平均场理论,并支持流模型的加拉沃蒂推测.
科学领域:
- 流体动力学 流体动力学
- 统计力学 统计力学
- 计算物理 计算物理
背景情况:
- 可逆的纳维埃-斯托克斯 (RNS) 方程通过通过动态粘度保持恒定的能量或度来修改消耗性NS方程.
- 之前的光谱直接数值模拟探索了RNS,但对参数模式有局限性.
研究的目的:
- 调查一个线性,强迫的RNS系统,使用Fourier空间中的日志格子来提高分辨率.
- 探索超出先前模拟范围的参数模式.
- 检查相位过渡,并验证RNS模型的加拉沃蒂假设.
主要方法:
- 将RNS方程投射到日志格子上,用于光谱模拟.
- 在极高分辨率下进行数值模拟.
- 分析了使用非尺寸化的强迫和质作为参数的相位过渡.
- 将RNS和NS统计数据进行比较,以测试Gallavotti猜测的调整.
主要成果:
- 证实了二次阶段过渡,很好地描述了平均场兰道理论.
- 在较低的分辨率下观察到一个不完美的过渡,偏离了平均场预测.
- 发现与1D可逆Leith流模型的质量一致.
- 在RNS和NS模型之间统计等效的推导条件.
结论:
- 高分辨率的日志格模拟显示了RNS系统中的相位过渡.
- 结果支持了加拉沃蒂猜测,显示了非平衡系统中平均数量的集体等价性.
- 该研究强调了解决方案对过渡特征的影响.
相关概念视频
01:28Navier–Stokes Equations
588
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
588
01:25Poisson's And Laplace's Equation
3.1K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
3.1K
01:17Steady, Laminar Flow Between Parallel Plates
243
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
243
01:24Reynolds Transport Theorem
1.2K
The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit...
1.2K
01:10Poiseuille's Law and Reynolds Number
6.7K
Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:
6.7K
01:22Eulerian and Lagrangian Flow Descriptions
1.5K
Fluid flow analysis is critical in many scientific and engineering disciplines, and two principal approaches are used to describe this flow: the Eulerian and Lagrangian methods. These methods offer different perspectives on monitoring and analyzing the motion of fluids, each with distinct advantages depending on the scenario.
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
The Eulerian method focuses on fixed points in space where fluid properties, such as velocity, pressure, and temperature, are observed as the fluid moves between these...
1.5K