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Unformatted text preview: Lecture Notes in Incompressible Fluid Dynamics: Phenomenology, Concepts and Analytical Tools. Jacques Lewalle Syracuse University 2 c Jacques Lewalle 2006 Contents 0.1 What is different about these notes? . . . . . . . . . . . . . . 9 0.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 0.2.1 Part I: Introduction . . . . . . . . . . . . . . . . . . . . 13 0.2.2 Part II: Basic concepts and equations . . . . . . . . . . 14 0.2.3 Part III: Approximations . . . . . . . . . . . . . . . . . 14 1 Motivation 17 1.1 Internal Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.1.1 A simple problem . . . . . . . . . . . . . . . . . . . . . 17 1.1.2 Entrance flow . . . . . . . . . . . . . . . . . . . . . . . 19 1.1.3 Transition to turbulence . . . . . . . . . . . . . . . . . 21 1.1.4 Pipe exit and secondary flow . . . . . . . . . . . . . . . 24 1.1.5 Advanced problems . . . . . . . . . . . . . . . . . . . . 25 1.1.6 Food for thought . . . . . . . . . . . . . . . . . . . . . 25 1.2 External flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.2.1 Control volume analysis . . . . . . . . . . . . . . . . . 27 1.2.2 Potential flow model . . . . . . . . . . . . . . . . . . . 29 1.2.3 Phenomenology . . . . . . . . . . . . . . . . . . . . . . 29 1.2.4 Food for thought . . . . . . . . . . . . . . . . . . . . . 30 1.3 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2 Kinematics 35 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.1.1 Intrinsic notations . . . . . . . . . . . . . . . . . . . . 36 2.1.2 Component notations . . . . . . . . . . . . . . . . . . . 37 2.1.3 Index notations . . . . . . . . . . . . . . . . . . . . . . 39 2.2 Eulerian vs. Lagrangian descriptions . . . . . . . . . . . . . . 41 2.2.1 Lagrangian description of motion . . . . . . . . . . . . 44 2.2.2 Eulerian description . . . . . . . . . . . . . . . . . . . 45 3 4 CONTENTS 2.2.3 Pathlines, streaklines and streamlines . . . . . . . . . . 49 2.2.4 Caution! . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.3 Differential concepts and their geometry . . . . . . . . . . . . 56 2.3.1 Differentials and vectors . . . . . . . . . . . . . . . . . 56 2.4 Mass balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.1 Vector potential and stream function . . . . . . . . . . 59 2.5 Flow about a point: Helmholtz . . . . . . . . . . . . . . . . . 60 2.5.1 Rate of strain . . . . . . . . . . . . . . . . . . . . . . . 61 2.5.2 Local rotation and vorticity . . . . . . . . . . . . . . . 63 2.6 Kinematic decompositions of a velocity field . . . . . . . . . . 64 2.7 Vorticity, , - 2 , etc. . . . . . . . . . . . . . . . . . . . . . 66 2.7.1 Biot-Savart relation . . . . . . . . . . . . . . . . . . . . 66 2.7.2 Vorticity, streamfunctions, and more . . . . . . . . . . 68 2.7.3 Vorticity and boundary conditions . . . . . . . . . . . . 69 2.7.4 Discrete vortices vs. continuous vorticity . . . . . . . .....
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fluidsToc - Lecture Notes in Incompressible Fluid Dynamics:...

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