SG3122 Wave Motions and Hydrodynamic Stability 7.5 credits
Vågrörelser och hydrodynamisk stabilitet
The course is optional from all engineering programes and is addressed to graduate (SG3122) and undergraduate (SG2221) students with fundamental knowledge and interest in fluid dynamics. The course is recommended to students following the Masters of Science in Engineering Mechanics programme. The extra work required for graduate students is found under Examination.
The student will acquire knowledge in fundamental concepts and phenomena in wave motions in fluids and hydrodynamic instabilities. It will help you to understand the theory underlying some commonly observed flow phenomena considered during the course.
Educational levelThird cycle
Academic level (A-D)D
Information for research students about course offerings
See KTH-schedule for period 2.
The student will acquire knowledge in fundamental concepts and phenomena in wave motions in fluids and hydrodynamic instabilities. It will help you to understand the theory underlying some commonly observed flow phenomena, such as
- why the surface waves behind a boat have a limited spreading angle
- why the wake of a cylinder beats at a fixed frequency independently of the external disturbances
- why Tsunamis arise and how they behave when approaching the shore
- why the so spectacular Billow clouds in the atmosphere are formed
Course main content
After completing this course the student should be able to
- describe the behaviour of surface gravity waves
- explain the concept of group velocity of a wave
- describe the main features of internal waves in continuously stratified fluids, such as the oceans and in the atmosphere
- identify the mechanisms behind instabilities in flows governed by thermal convection and heat exchange
- discuss effects of centrifugal and Coriolis forces in unstable rotating systems
- describe the instability nature and mechanisms in shear flows, i.e. wake, jet, boundary layer and channel flows
- discuss the influence of viscosity on stability
- explain why classic asymptotic stability analysis provides only a partial description of disturbance amplification in shear flows
The teaching is deliverd by means of a mixture between traditional classroom teaching and seminar-based lectures where open discussions will be promoted by student-active-elements such as gobbets. Furhtermore, table experiments will be shown during classes in order to demonstrate and clarify parts of the surveyed theory. In order to activate the students to develop practical skills one experimental and one numerical assignment are given in this course. Each lecture will begin with a few minutes review and discussion of last lecture's content. The total amount of lecture hours is 42h, which are delivered over 21 gatherings (i.e. 2h per lecture).
A course in Fluid Dynamics.
- Acheson D.J., Elementary Fluid Dynamics, Oxford University Press, USA, 1990 (ISBN 0198596790).
- Kundu P.K. & Cohen I.M., Fluid Mechanics, Elsevier Academic Press, USA, 2004 (ISBN 0121782530).
- Your own lecture notes and other distributed material.
The examination is composed of an alternating oral and written test. The test is usually performed in groups of two students and will last for about 45 minutes, including the presentation of the numerical assignment. A list of about 50 questions will be available from the course home page from where questions will be taken and asked at the individual test.
Requirements for final grade
The following three items have to be approved in order to obtain a pass of the course (7.5c):
- One laboration with adherent preparation tasks and lab report (for graduate students the lab report has to be an extended version) Experimental analysis of Tollmien-Schlichting waves over a flat plate(1.5c)
- One home assignment with report (for graduate students some Matlab programming is required and the presentation at the oral exam has to be an extended version) Numerical computation of flow instability for different configurations (1.5c)
- Oral/written examination (4.5c)
All items are graded. For graduate students the highest grade is required to obtain a pass.
Jens Fransson, Luca Brandt
Jens Fransson, Luca Brandt
The course is given in English.
Course plan valid from: Autumn 10.