Physical Fluid Mechanics
This course is an introduction to the physics of fluids — how liquids and gases move, deform, and exert forces. Unlike engineering courses that focus on design formulas, this course prioritizes physical reasoning, conceptual clarity, and the intuitive understanding of flow phenomena.
We will explore questions drawn from both controlled laboratory experiments and nature itself: Why does stirring a cup of coffee create a dimple at the center? Why do tea leaves always gather at the bottom center of a stirred cup? How can a tiny water strider walk on a pond? Why does a spinning ball curve in flight? What keeps a hurricane spinning for days, and why does it have an eye?
Through these tangible examples, we build a systematic physical framework based on conservation laws (mass, momentum, and energy) and the continuum hypothesis — the idea that we can treat fluids as continuous media rather than collections of molecules.
The mathematical level is kept at multivariable calculus and ordinary differential equations. Every equation we introduce will be thoroughly interpreted in plain physical terms before any derivation begins. The goal is not to produce expert solvers of complex PDEs, but to train students to see the physics hidden inside the mathematics — and to confidently estimate, approximate, and reason about any fluid flow they encounter, whether in the lab, in the atmosphere, or in the ocean.
We will explore questions drawn from both controlled laboratory experiments and nature itself: Why does stirring a cup of coffee create a dimple at the center? Why do tea leaves always gather at the bottom center of a stirred cup? How can a tiny water strider walk on a pond? Why does a spinning ball curve in flight? What keeps a hurricane spinning for days, and why does it have an eye?
Through these tangible examples, we build a systematic physical framework based on conservation laws (mass, momentum, and energy) and the continuum hypothesis — the idea that we can treat fluids as continuous media rather than collections of molecules.
The mathematical level is kept at multivariable calculus and ordinary differential equations. Every equation we introduce will be thoroughly interpreted in plain physical terms before any derivation begins. The goal is not to produce expert solvers of complex PDEs, but to train students to see the physics hidden inside the mathematics — and to confidently estimate, approximate, and reason about any fluid flow they encounter, whether in the lab, in the atmosphere, or in the ocean.
讲师
日期
2026年09月21日 至 2027年01月11日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一 | 09:50 - 12:15 | Shuangqing | Zoom 15 | 204 323 0165 | BIMSA |
修课要求
Mathematics: Multivariable calculus (gradient, divergence, curl), basic ODEs, and familiarity with vector notation. Physics: General physics I (Newton's laws, work-energy theorem, hydrostatics basics) and thermodynamics (temperature, pressure, and equation of state at a conceptual level).
课程大纲
Week 1
Topic: Continuum Hypothesis & Fluid Properties
Key Physical Concepts: What defines a fluid; density, pressure, temperature, viscosity; molecular vs. macroscopic views. Surface tension and capillary effects.
Anchoring Experiment/Phenomenon: Surface tension: water strider walking on water; why raindrops are spherical.
Week 2--3
Topic: Kinematics --- Describing Motion
Key Physical Concepts: Lagrangian vs. Eulerian descriptions; material derivative; deformation (stretching, shearing, rotation); vorticity and divergence.
Anchoring Experiment/Phenomenon: Dye streak visualization; bathtub vortex --- tracking fluid parcels and observing rotational motion.
Week 4
Topic: Fluid Statics
Key Physical Concepts: Pressure distribution; Pascal's law; Archimedes' principle; surface tension and capillary action.
Anchoring Experiment/Phenomenon: Why icebergs float; capillary rise in thin tubes; soap bubbles.
Week 5--6
Topic: Bernoulli Equation & Inviscid Flow
Key Physical Concepts: Energy conservation along a streamline; pressure--velocity tradeoff; limitations of Bernoulli's principle.
Anchoring Experiment/Phenomenon: Curveball / Magnus effect; airplane lift (debunking "equal transit time"); Venturi meter.
Week 7--8
Topic: Navier--Stokes Equations --- Physical Meaning
Key Physical Concepts: Stress tensor; Newton's viscosity law; term-by-term physical interpretation; Reynolds number;
Anchoring Experiment/Phenomenon: Tea leaf paradox --- shows how pressure gradients and boundary layers produce secondary flows.
Week 9
Topic: Exact Viscous Solutions & Laboratory Observation
Key Physical Concepts: Couette flow (shear-driven) and Poiseuille flow (pressure-driven); velocity profiles and flow rate.
Anchoring Experiment/Phenomenon: Honey pouring vs. water; artery blood flow as pulsatile Poiseuille flow. Laboratory visit: tour of the Peking University low-turbulence water tunnel, introducing experimental fluid mechanics and flow measurement techniques (Hydrogen bubble visualization).
Week 10
Topic: Vorticity and Circulation Dynamics
Key Physical Concepts: Vorticity transport; Kelvin's circulation theorem; vortex stretching; Helmholtz's laws.
Anchoring Experiment/Phenomenon: Hurricane intensification (vortex stretching); draining sink; wingtip vortices behind aircraft.
Week 11
Topic: Boundary Layer Theory
Key Physical Concepts: Prandtl's boundary layer concept; no-slip condition; flow separation; form drag vs. skin friction.
Anchoring Experiment/Phenomenon: Golf ball dimples (turbulent boundary layer delays separation, reducing drag); why streamlined bodies have low drag.
Week 12
Topic: Dimensional Analysis & Scaling
Key Physical Concepts: Buckingham Pi theorem; physical meaning of Reynolds, Froude, Weber, and Mach numbers; scaling laws.
Anchoring Experiment/Phenomenon: Scaling model tests in wind tunnels; why large animals and small insects experience flow differently (Re ~ 10⁷ for whale vs. Re ~ 10⁻² for bacterium).
Week 13
Topic: Instability & Transition to Turbulence
Key Physical Concepts: Physical mechanisms of instability; Kelvin--Helmholtz instability; Rayleigh--Bénard convection; energy cascade.
Anchoring Experiment/Phenomenon: Billow clouds (K-H instability); convection cells; transition from laminar to turbulent flow.
Week 14
Topic: Compressible Flow & Hypersonic Flow Phenomena
Key Physical Concepts: Mach number; compressibility effects; shock waves; density variations; aerodynamic heating in high-speed flows.
Anchoring Experiment/Phenomenon: Rayleigh scattering flow visualization (hypersonic): visualization of hypersonic boundary-layer structures and transition processes through temperature-dependent CO₂ condensation and laser scattering.
Week 15
Topic: Advanced Flow Visualization Techniques in Hypersonic Flows
Key Physical Concepts: Optical diagnostics for compressible flows; density gradients; temperature measurements; coupling between flow structures and aerodynamic heating.
Anchoring Experiment/Phenomenon: Laboratory visit: tour of the Peking University hypersonic quiet wind tunnel, introducing hypersonic experimental facilities and advanced aerodynamic research. High-speed schlieren: visualization of density-gradient fields through refractive-index variations. Infrared thermography: measurement of model surface temperature rise and aerodynamic heating, including shear heating and dilatation heating.
Week 16
Topic: Special Topics & Laboratory Integration
Key Physical Concepts: Review and integration of fundamental concepts; connecting laboratory observations with conservation laws, scaling analysis, and flow physics.
Anchoring Experiment/Phenomenon: Student discussion: from incompressible laboratory flows to hypersonic flows.
Topic: Continuum Hypothesis & Fluid Properties
Key Physical Concepts: What defines a fluid; density, pressure, temperature, viscosity; molecular vs. macroscopic views. Surface tension and capillary effects.
Anchoring Experiment/Phenomenon: Surface tension: water strider walking on water; why raindrops are spherical.
Week 2--3
Topic: Kinematics --- Describing Motion
Key Physical Concepts: Lagrangian vs. Eulerian descriptions; material derivative; deformation (stretching, shearing, rotation); vorticity and divergence.
Anchoring Experiment/Phenomenon: Dye streak visualization; bathtub vortex --- tracking fluid parcels and observing rotational motion.
Week 4
Topic: Fluid Statics
Key Physical Concepts: Pressure distribution; Pascal's law; Archimedes' principle; surface tension and capillary action.
Anchoring Experiment/Phenomenon: Why icebergs float; capillary rise in thin tubes; soap bubbles.
Week 5--6
Topic: Bernoulli Equation & Inviscid Flow
Key Physical Concepts: Energy conservation along a streamline; pressure--velocity tradeoff; limitations of Bernoulli's principle.
Anchoring Experiment/Phenomenon: Curveball / Magnus effect; airplane lift (debunking "equal transit time"); Venturi meter.
Week 7--8
Topic: Navier--Stokes Equations --- Physical Meaning
Key Physical Concepts: Stress tensor; Newton's viscosity law; term-by-term physical interpretation; Reynolds number;
Anchoring Experiment/Phenomenon: Tea leaf paradox --- shows how pressure gradients and boundary layers produce secondary flows.
Week 9
Topic: Exact Viscous Solutions & Laboratory Observation
Key Physical Concepts: Couette flow (shear-driven) and Poiseuille flow (pressure-driven); velocity profiles and flow rate.
Anchoring Experiment/Phenomenon: Honey pouring vs. water; artery blood flow as pulsatile Poiseuille flow. Laboratory visit: tour of the Peking University low-turbulence water tunnel, introducing experimental fluid mechanics and flow measurement techniques (Hydrogen bubble visualization).
Week 10
Topic: Vorticity and Circulation Dynamics
Key Physical Concepts: Vorticity transport; Kelvin's circulation theorem; vortex stretching; Helmholtz's laws.
Anchoring Experiment/Phenomenon: Hurricane intensification (vortex stretching); draining sink; wingtip vortices behind aircraft.
Week 11
Topic: Boundary Layer Theory
Key Physical Concepts: Prandtl's boundary layer concept; no-slip condition; flow separation; form drag vs. skin friction.
Anchoring Experiment/Phenomenon: Golf ball dimples (turbulent boundary layer delays separation, reducing drag); why streamlined bodies have low drag.
Week 12
Topic: Dimensional Analysis & Scaling
Key Physical Concepts: Buckingham Pi theorem; physical meaning of Reynolds, Froude, Weber, and Mach numbers; scaling laws.
Anchoring Experiment/Phenomenon: Scaling model tests in wind tunnels; why large animals and small insects experience flow differently (Re ~ 10⁷ for whale vs. Re ~ 10⁻² for bacterium).
Week 13
Topic: Instability & Transition to Turbulence
Key Physical Concepts: Physical mechanisms of instability; Kelvin--Helmholtz instability; Rayleigh--Bénard convection; energy cascade.
Anchoring Experiment/Phenomenon: Billow clouds (K-H instability); convection cells; transition from laminar to turbulent flow.
Week 14
Topic: Compressible Flow & Hypersonic Flow Phenomena
Key Physical Concepts: Mach number; compressibility effects; shock waves; density variations; aerodynamic heating in high-speed flows.
Anchoring Experiment/Phenomenon: Rayleigh scattering flow visualization (hypersonic): visualization of hypersonic boundary-layer structures and transition processes through temperature-dependent CO₂ condensation and laser scattering.
Week 15
Topic: Advanced Flow Visualization Techniques in Hypersonic Flows
Key Physical Concepts: Optical diagnostics for compressible flows; density gradients; temperature measurements; coupling between flow structures and aerodynamic heating.
Anchoring Experiment/Phenomenon: Laboratory visit: tour of the Peking University hypersonic quiet wind tunnel, introducing hypersonic experimental facilities and advanced aerodynamic research. High-speed schlieren: visualization of density-gradient fields through refractive-index variations. Infrared thermography: measurement of model surface temperature rise and aerodynamic heating, including shear heating and dilatation heating.
Week 16
Topic: Special Topics & Laboratory Integration
Key Physical Concepts: Review and integration of fundamental concepts; connecting laboratory observations with conservation laws, scaling analysis, and flow physics.
Anchoring Experiment/Phenomenon: Student discussion: from incompressible laboratory flows to hypersonic flows.
参考资料
Primary: Fluid Mechanics by Kundu, Cohen & Dowling — we focus on explanatory sections and figures.
For intuition: Physical Fluid Dynamics by D.J. Tritton — rich in experimental observations.
For natural phenomena: Fluid Dynamics of the Atmosphere and Ocean by G.K. Vallis (selected chapters) — accessible for undergraduates.
Supplemental video library: We will use MIT's Fluid Mechanics lecture videos and the BBC/NOAA visual archives of atmospheric and oceanographic flows.
For intuition: Physical Fluid Dynamics by D.J. Tritton — rich in experimental observations.
For natural phenomena: Fluid Dynamics of the Atmosphere and Ocean by G.K. Vallis (selected chapters) — accessible for undergraduates.
Supplemental video library: We will use MIT's Fluid Mechanics lecture videos and the BBC/NOAA visual archives of atmospheric and oceanographic flows.
听众
Undergraduate
视频公开
公开
笔记公开
公开
讲师介绍
李存标，1984年在南京航空航天大学获得本科学位，1990年在中国科学院力学研究所获得硕士学位，1995年在北京航空航天大学获得博士学位。1995年，他在中国科学院大气物理研究所开始博士后研究，并于1998年成为清华大学副教授。2001年加入北京大学湍流与复杂系统国家重点实验室后，李存标晋升为教授。他已发表100余篇技术论文，出版4部著作，并作过100余场受邀讲座与学术报告。2005年，他获得“国家杰出青年科学家奖”基金。他任湍流与复杂系统国家重点实验室主任，并担任《Physics of Fluids》编辑顾问委员会成员（Editorial Advisory Board Member），此前曾担任《Experiments in Fluids》编辑顾问委员会成员。其研究兴趣包括边界层转捩、高超声速边界层不稳定性、水中薄盘自由下落动力学、近壁区PIV测量以及非线性波相互作用。作为AIAA会员，李存标牵头了多项国家重大项目，尤其是在高超声速静音风洞的研发方面；同时也参与多个国家级科学委员会工作。他目前担任《AIAA Journal》副编辑（Associate Editor）。