Course Description:

This is a preparatory course for students who will continue pursuing advanced topics of fluid physics and modeling. The course content is designed to familiarize the students with the fundamental equations governing most of the flow problems in science and engineering. The underlying physics behind the mathematics will be emphasized. Analytical solutions for some flows are then introduced. More advanced topics, including vortex kinematics and dynamics, turbulence, and free-surface flows, will be included when class schedule permits.

Prerequisites:
	No previous knowledge of fluid mechanics or undergraduate course on fluid mechanics is needed. Multivariable Calculus plus an undergraduate course of Applied Mathematics or Engineering Mathematics on vector analyses and ordinary differential equation, however, are required. 本課程無需先修其他基礎流體力學課程，但是需修畢微積分以及內容包括向量分析、常微分方程式、傅立葉分析、線性偏微分方程式 的工程數學或應用數學課程

Grading: Based on the grades of homework and two quizzes.

Online classroom:

Tentative Schedule:

	Topics	Reading	Supplement Materials	Homework
1	Fundamental Methods and Tools • Continuum hypothesis • Eulerian vs Lagrangian coordinates • Material derivative • Control vs system volumes - Reynolds' transport theorem	(Currie) 1.1 1.2 1.3 1.4 1.5	• NCFMF film on Eulerian & Lagrangian description   (note ) • Fluid as a continuum • Introduction to tensors • Einstein summation convention: an introduction • Einstein notation: proofs, examples, and Kronecker delta • Kronecker delta and Levi-Civita symbol
2	Governing Equations • Conservation of mass - continuity equation • Conservation of momentum • Deformation (rotation and shear) • Constitutive equations	1.6 1.7  1.9 1.10 1.11	• NCFMF film on deformation of continuous media   (note ) • Movie shows rotational vs irrotational flow (shorter version)
3	• Viscosity coefficients • Navier-Stokes equations • Boundary conditions	1.12 1.13 1.16	• Movies demonstrates non-Newtonian fluid: 1,  2,  3,  4,  5 • Discussions on Stokes' hypothesis: (1) Gad-el-Hak, M.,1995, Questions in fluid mechanics: Stokes’ hypothesis for a Newtonian, isotropic fluid, J. Fluids Eng. 117(1), 3-5. (pdf1 or pdf2 ) (2) Buresti, G. 2015, A note on Stokes' hypothesis, Acta Mech., 226, 3555-3559. (pdf ) • Movie demonstrates no-slip condition • Darrigol, O., 2002, Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes Equation, Archive for History of Exact Sciences, 56, 95-150. (pdf ) • Cannone, M. and Friedlander, S., 2003, Navier: blow-up and collapse, Notices of the American Mathematical Society, 50, 7-13. (pdf )
4	• Conservation of energy • Thermal and mechanical energy equations	1.8 1.14
5	Exact Solutions for Viscous Laminar Flows of Incompressible Fluids • Couette flow • Poiseuille flow • Governing equations in cylindrical coordinate system	(Currie) 7.1 7.2	• Why laminar flow is AWESOME • Turbulent flow is MORE awesome than laminar flow • See below for some interesting reading on Couette flow and Poiseuille flow
6	• Circular Couette flow • Stokes' first problem • Stokes' second problem	7.3 7.4 7.5	• Movies demonstrate reversible laminar flow (circular Couette flow): 1,   2,   3
7	Boundary Layers • Boundary-layer thickness • Boundary-layer equations	(Currie) 9.1 9.2	• NCFMF film on fundamentals of boundary layers   (note ) • Prandtl, L., 1904, Über Flüssigkeitsbewegung bei sehr kleiner Reibung, Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg, S. 484-491   (English translation from NACA )
8	• Blasius solution of boundary-layer equations for a flat surface	9.3	• Blasius, H., 1908, Grenzschichten in Flüssigkeiten mit kleiner Reibung, Z. Math. Phys. 56, 1–37. (English translation from NACA ) • Hager, W.H., 2003, Blasius: a life in research and education, Exp. Fluids, 34(5), 566-571 • About Heinrich Blasius
9	• Approximate solution for flat surface -momentum integral equation • General momentum integral equation of boundary layer	9.8 9.9
10	• Kármán-Pohlhausen approximation • Boundary-layer separation	9.10 9.11	• von Kármán, T. 1921, Über laminare and turbulent Retbung, Z. Angew. Math. Mech., 1(4), 233-252.   (English translation from NACA: On laminar and turbulent friction ) • Pohlhausen, K. 1921, Zur näherungsweisen Integration der Differentialgleichung der Iaminaren Grenzschicht, Z. Angew. Math. Mech., 1(4), 252-290.    (English translation: The approximate integration of the differential equation of the laminar boundary layer ) • Boundary layer separation and stall • NCFMF film on Boundary Layers Control
11	• Stability of boundary layer	9.12	• NCFMF film on flow instabilities   (note ) • Heisenberg, W. 1924, Über Stabilität und Turbulenz von Flüssigkeitsströmen, Annalen der Physik, 379(15), 577-627.   (English translation from NACA: On stability and turbulence of fluid flows ) • Eckert, M. 2010, The troublesome birth of hydrodynamic stability theory: Sommerfeld and the turbulence problem, Eur. Phys. J. H 35, 29–51.
12	Flow Kinematics • Flow lines • Circulation and vorticity • Kinematics of vortex lines (Helmholtz theorem of vorticity) • Kelvin's theorem of circulation	(Currie) 2.1 2.2 2.4 3.1
13	Special Forms of the Governing Equation • Vorticity equation • Bernoulli equation	(Currie) 3.4 3.2
14	Ideal-Fluid Flow (Tow-Dimensional) • Stream function, complex potential and complex velocity • Uniform flow and flows of sink, source, vortex and doublet • Flow around a circular cylinder without circulation • Flow around a circular cylinder with circulation	(Currie) 4.1  4.2 4.3  4.4  4.7 4.8 4.9	• Potential Flow Simulator
15	Dynamical Similarity and Dimensional Analysis • Non-dimensional parameters determined from differential equation • Dimensional matrix • Buckingham's Pi theorem • Dynamical similarity	(Kundu) 8.1  8.2 8.3 8.4 8.5 8.6 8.7	• Buckingham's original papers:   Buckingham, E., 1914, On physically similar systems; illustrations of the use of dimensional equations, Physical Review, 4(4), 345-376.   Buckingham, E., 1915, Model experiments and the forms of empirical equations, American Society of Mechanical Engineers, Transactions, 37, 263-292. • A mechanical engineer's view: pdf   Sonin, A.A., 2001, The physical basis of dimensional analysis  • A physical oceanographer's view: 2005 essay   Price, J.F., 2003, Dimensional analysis of models and data sets, Am. J. Phys. 71(5), 37-447 • A mathematician's view: 2009 lecture note   Hunter, J.K., 2009, Dimensional analysis, scaling, and similarity
16	Turbulence (An introduction) • Averaging • Correlations and spectra • Reynolds averaged equations of motion	(Kundu) 12.1 12.2 12.3 12.4 12.5	• NCFMF film on turbulence   (note ) • Movie demonstrates laminar vs turbulent flow 1 • Movie demonstrates laminar vs turbulent flow 2 • Movie demonstrates transition from laminar to turbulent flow • Turbulent Flow is MORE Awesome Than Laminar Flow • Turbulent boundary layer from direct numerical simulation
17	• Kinetic energy budget of mean flow • Kinetic energy budget of turbulent flow • Turbulence production and cascade	12.6 12.7 12.8  12.9
18	• Wall-free turbulent shear flow • Wall-boundary turbulent shear flow	12.10 12.11
19	Surface Waves (An introduction) • Boundary conditions between immiscible fluids • Gravity surface waves - ideal flow and linearization • Influence of surface tension • Group velocity, energy flux, and dispersion • Nonlinear effects in shallow and deep Water • The Stokes drift	(Kundu) 7.2 7.3 7.5 7.6	• Stokes, G.G. 1847, On the theory of oscillatory waves, Transactions of the Cambridge Philosophical Society, 8, 441-455 • Stokes, G.G. 1880, Supplement to a paper on the Theory of Oscillatory Waves. In Mathematical and Physical Papers, 314-326 • Movie demonstrates dispersion of water wave

Useful materials
     • National Committee for Fluid Mechanics Films (NCFMF) (MIT)  also see the NSF Film series in YouTube
     • Illustrated Experiments in Fluid Mechanics: The NCFMF Book of Film Notes (MIT)
     • Classic and Historical Papers in Geophysical Fluid Dynamics and Atmospheric and Oceanic Dynamics  (by G.K Vallis of Exeter University)
     • Greek alphabets

Osborne Reynolds (1842-1912)

• Reynolds O. 1883. An experimental investigation of the circumstances which determine whether the motion of water in parallel channels shall be direct or sinuous and of the law of resistance in parallel channels. Philos. Trans. R. Soc. 174, 935-982 (pdf )      • Reynolds O. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc. 186,123-164 (pdf )      • "Osborne Reynolds: Scientist, Engineer and Pioneer" (Jackson, J.D., 1995, Proc. R. Soc. Lond. A, 451, 49-86)      •  "Note on the History of the Reynolds Number" (Rott, N., 1990, Annu. Rev. Fluid Mech., 22, 1-12) (pdf )      • "Osborne Reynolds and the Publication of His Papers on Turbulent Flow" (Jackson, D. and Launder, B., 2007, Annu. Rev. Fluid Mech., 39 19-35) (pdf )       • "Collected Papers on Mechanical and Physical Subjects", in three volumes, in digital format: volume 1, volume 2, volume 2

Ludwig Prandtl (1876-1953)

• A short collection of biographical and technical links about Ludwig Prandtl      • In 1904, Prandtl delivered a lecture entitled "On the motion of fluids of very small viscosity" to the 3rd International Mathematical        Congress in Heidelberg, and introduced the concept of boundary layer.        (NACA Technical Memorandum 452: English translation of the original paper: "Über Flüssigkeitsbewegung bei sehr kleiner Reibung",         Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg, 1904, S. 484-491)      • Anderson, J.D., 2005, Ludwig Prandtl's Boundary Layer, Physics Today, Dec. 2005, 42-48      • "Ludwig Prandtl - A Biographical Sketch, Remembrances and Documents"  (authored by his daughter Johanna Vogel-Prandtl)      • Ludwig Prandtl in Wikipedia

Geoffrey Ingram Taylor (1886-1975)

• Biography of G.I. Taylor      • "The Life and Legacy of G.I. Taylor", Cambridge University Press, 1994  (by G.B. Batchelor)      • G.I. Taylor demonstrated low-Reynolds-Number Flows  (NCFMF film from MIT)      • Classical Physics Through the Work of GI Taylor  (a course at Harvard)      • "Modern Classical Physics Through the Work of G.I. Taylor"  (an article in Physics Today about the course above)      • G.I. Taylor in Wikipedia

Some interesting readings on Couette flow
     • Donnelly, R.J., 1991, Taylor-Couette flow: the early days, Phys. Today ,44(11), 32-39
     • Piau, J.M., Bremond, M., Couette, J.M. & Piau, M., 1994, Maurice Couette, one of the founders of rheology, Rheol. Acta, 33, 357-368
     • Dontula, P., Macosko, C.W. & Scriven, L.E., 2005, Origin of concentric cylinder viscometry, J. Rheol., 49, 807-818
     • Piau, J.M. & Piau, M., 2005, Letter to the Editor: Comment on “Origin of concentric cylinder viscometry” [J. Rheol. 49, 807–818 (2005)].
         The relevance of the early days of viscosity, slip at the wall, and stability in concentric cylinder viscometry, J. Rheol. 49, 1539-1550

Some interesting readings on Poiseuille flow
     • A blog on Jean Leonard Marie Poiseuille
     • Brillouin, M., 1930, Jean Leonard Marie Poiseuille, J. Rheol., 1, 345-348
     • Herrick, J.F., 1942, Poiseuille's observations on blood flow lead to a law in hydrodynamics, Am. J. Phys., 10, 33-39
     • Pfitzner J., 1976, Poiseuille and his law, Anaesthesia, 31, 273-275
     • Sutera, S.P. & Skalak, R.,1993, The History of Poiseuille's Law, Annu.Rev. Fluid Mech., 25, 1-20 

Classic textbooks of Fluid Mechanics
     • Batchelor, G.B., An Introduction to Fluid Dynamics, Cambridge University Press, 1967  (Google book, Amazon)
     • Landau, L.D. & Lifshitz, E.M., Fluid Mechanics, Pergamon, 1959  (Amazon)
     • Prandtl, L. (expanded by H. Oertel), Essentials of Fluid Mechanics, Springer, 2010  (Chapter 1 Introduction, Amazon)

Other good textbooks of Fluid Mechanics
     • Acheson, D.J., Elementary Fluid Dynamics, Oxford University Press, 1990  (Google book, Amazon)
     • Faber, T.E., Fluid Dynamics for Physicists, Cambridge University Press, 1995  (Google book, Amazon)
     • Smith, C.R., Introduction to Graduate Fluid Mechanics, Self published, 2019
     • Smyth, W.R., All Things Flow: Fluid Mechanics for the Natural Sciences, 2019

Books with pictures
     • Van Dyke, M., An Album of Fluid Motion, Parabolic Press, 1982  (Amazon)
     • Samimy, M, Breuer, K.S., Leal, L.G. & Steen, P.H., A Gallery of Fluid Motion, Cambridge University Press, 2004  (Google book, Amazon)

Visualization of fluid flow
     • efluids media galleries
     • Flow Visualization: Art and Physics
     • Flow Visualization

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