不平衡组合的等价性:双维流与双级联流的二维流
Maheswar Maji1, Karthik Subramaniam Eswaran1, Sourangshu Ghosh2
1Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur-721 302, India.
Physical review. E
|August 16, 2023
概括
我们表明,一个时间可逆的纳维埃-斯托克斯方程准确地模拟了二维的流. 这证实了不平衡集对乱系统中保存能量和的等价性推测.
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:
- 两个维度中的流表现出双级联的行为.
- 不平衡集的等价性是统计力学中的一个关键猜想.
- 标准的纳维埃-斯托克斯方程描述了流体运动,但不是时间可逆的.
研究的目的:
- 为了研究2D流的非平衡集合等价性推测.
- 构建和分析一个正式时间可逆的纳维埃-斯托克斯方程.
- 将统计属性与标准的纳维埃-斯托克斯模拟进行比较.
主要方法:
- 构建一个时间可逆的纳维埃-斯托克斯方程与全球的能量和天体保护约束.
- 对标准方程和时间可逆方程的解的统计性质进行比较分析.
- 一点和两点测量用于评估流动特性.
主要成果:
- 正式的时间可逆系统成功地复制了2D流的特征.
- 在统计学量方面,对于反流和直流布区域都达成了很好的协议.
- 集体等价的猜想在有限的雷诺兹数下对保存的能量和质量保持良好.
结论:
- 正式时间可逆的纳维埃-斯托克斯方程为二维流提供了一个有效的模型.
- 这项研究支持在这种情况下,不平衡集体等价的猜想.
- 对于能量和质保存的流量来说,这些发现很强大.
相关概念视频
01:22Couette Flow
323
Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
323
01:17Steady, Laminar Flow Between Parallel Plates
237
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.
237
02:20Dynamic Equilibrium
51.9K
A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
51.9K
01:15Dimensionless Groups in Fluid Mechanics
367
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
367
01:30Typical Model Studies
382
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
382
01:24Turbulent Flow
216
Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
216