流体力学方程讲义Stephen_Childress.pdf

An Introduction to Theoretical Fluid Dynamics
Stephen Childress
February 12, 2008
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Notes on the course
The course meets on Wednesday, 9:20-11:30 am in Room 813 WWH.
Office Hours: TBA
BOOKS: The text is Landau and Lifshitz, Fluid Mechanics, available at the
Bookstore. Acheson’s Elementary Fluid Dynamics is a good elementary book.
The reserve books given below will be available in the Courant library.
Batchelor, . Introduction to Fluid Dynamics, Cambridge Univsrsity
• Press 1967
Landau and Lifshitz, Fluid Mechanis (2nd Ed.), Pergamon Press 1987.
•
Milne-Thomson, . Theoretical Hydrodynamics, McMillan (5th Ed.)
•
Lighthill, . An Informal Introduction to Theoretical Fluid Mechanics,
• Clarendon Press 1986.
Prandtl, L. Essentials of Fluid Dynamics, Hafner 1952.
•
Lamb, Hydrodynamics (6th Ed.), Cambridge University Press 1932
•
Courant and Freidrichs, Supersonic Flow and Shock Waves, Interscience
• 1948.
Meyer, An Introduction to Mathematical Fluids Dynamics, Dover 1971.
•
D. J. Acheson, Elementary Fluid Dynamics, Clarendon 1990.
•
Chapter 1
The fluid continuum
This course will deal with a mathematical idealization mon fluids such as
air or water. The main idealization is embodied in the notion of a continuum
and our “fluids” will generally be identified with a certain connected set of points
in RN , where we will consider dimension N to be 1,2, or 3. Of course the fluids
will move, so basically our subject is that of a moving continuum.
This description is an idealization which neglects the molecular structure of
real fluids. Liquids are fluids characterized by random motions of molecules on
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the scale of 10− 10− cm, and by a substantial resistance pression.
Gases consist of molecules− moving over much larger distances, with mean free
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paths of the order of 10− cm, and are pressed. Both liquids and
gases will fall within the scope of the theory of fluid motion which we will develop
below. The theory