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.
Lecturer
Date
21st September, 2026 ~ 11th January, 2027
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 09:50 - 12:15 | Shuangqing | Zoom 15 | 204 323 0165 | BIMSA |
Prerequisite
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).
Syllabus
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.
Reference
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.
Audience
Undergraduate
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Cunbiao Lee earned his undergraduate degree from the Nanjing University of Aeronautics and Astronautics in 1984, his master's degree from the Institute of Mechanics, Chinese Academy of Sciences, in 1990, and his Ph.D. from the Beijing University of Aeronautics and Astronautics in 1995. He began his postdoctoral fellowship at the Institute of Atmospheric Physics, Chinese Academy of Sciences, in 1995, and in 1998, became an associate professor at Tsinghua University. Lee was promoted to full professor after joining the State Key Laboratory for Turbulence and Complex Systems at Peking University in 2001. He has authored over 100 technical papers, 4 books, and delivered more than 100 invited lectures and seminars. In 2005, he received the National Outstanding Young Scientist Award. He serves as the director of the State Key Laboratory for Turbulence & Complex Systems and holds an Editorial Advisory Board member of Physics of Fluids, after serving on the Editorial Advisory Board member of Experiments in Fluids. His research interests include boundary-layer transition, hypersonic boundary-layer instability, dynamics of falling thin discs in water, near-wall PIV measurement, and nonlinear wave interaction. A member of the AIAA, Lee has spearheaded several major national projects, notably in the development of hypersonic quiet wind tunnels. He also participates in various major national science committees. He is an associated editor of AIAA J. now.