week1 - Fluid Dynamics 3 - 2011/2012 Jens Eggers...

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Unformatted text preview: Fluid Dynamics 3 - 2011/2012 Jens Eggers Preliminaries Course information Lecturer: Prof. Jens Eggers, Room SM2.3 Timetable: Weeks 1-12, Tuesday 2.00 (SM2), Thursday 4.10 (SM1) and Friday 11.10 (SM1). Course made up of 32 lectures. Office hours: my office hours for this course are Tuesday 3.00 in my room, SM2.3 Prerequisites: Mechanics 1, APDE2 and Calc2. Need ideas from vector calculus, complex function theory, separation solutions and PDEs. Homework: Questions from 10 worksheets set and marked during the course. Will be handed out each Friday, starting in the first week. Solutions to be returned the following Friday in the box marked Fluids3. Assessment: 2.5 hours exam in April, best 4 out of 5 questions. No calculators allowed. Credit points: will be awarded for serious attempts at 40% of homework. Only comes into play for exam marks in the range 30-40. Web: Standard unit description includes detailed course information. Also a fluids 3 web page ( http://www.maths.bris.ac.uk/~majge/fluids3.html ), which con- tains: Homework and solution sheets as well as lecture notes (will be put up on the web as soon as possible after each lecture). Lectures: There is no need to take notes during the lecture, as all material relevant for the exam will be put on the web. The main purpose of the lecture is the live development of the material, and a chance for you to ask questions! Recommended texts 1. A.R. Paterson, A First Course in Fluid Dynamics , Cambridge University Press. (The recommended text to complement this course - costs 50 from Amazon; there are 6 copies in Queens building Library and 3 copies in the Physics Library) 2. D.J. Acheson, Elementary Fluid Dynamics . Oxford University Press 3. L.D. Landau and E.M. Lifshitz, Fluid Mechanics . Butterworth Heinemann Films There is a very good series of educational films on Fluid Mechanics available on YouTube, produced by the National Committee for Fluid Mechanics Films in the US in the 1960s. Each film is also accompanied by a set of notes. I recommend them highly, and will point out the appropriate ones throughout this course. The following 3 sections are useful for the course. For the purposes of an examination, I would expect you to know the definition of div, grad, curl and the Laplacian in Cartesians and grad and the Laplacian in plane polars. Other definitions would be provided. Revision of vector operations Let u = ( u 1 , u 2 , u 3 ), v = ( v 1 , v 2 , v 3 ) be Cartesian vectors. Let ( x ) be a scalar function and f ( x ) = ( f 1 ( x ) , f 2 ( x ) , f 3 ( x )) a vector field of position x = ( x, y, z ) ( x 1 , x 2 , x 3 ). Then The dot product is u v = u 1 v 1 + u 2 v 2 + u 3 v 3 The cross (or vector) product is u v = ( u 2 v 3 u 3 v 2 ) x +( u 3 v 1 u 1 v 3 ) y +( u 1 v 2 u 2 v 1 ) z The gradient is = parenleftbigg x 1 , x 2 , x 3 parenrightbigg The divergence is...
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week1 - Fluid Dynamics 3 - 2011/2012 Jens Eggers...

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