SG2221 Wave Motions and Hydrodynamic Stability 7.5 credits

Vågrörelser och hydrodynamisk stabilitet

The course is optional from all engineering programmes and is addressed to graduate and undergraduate students with fundamental knowledge and interest in fluid dynamics.

The course is specially recommended to students following the Master of Science in Engineering Mechanics programme.

  • Education cycle

    Second cycle
  • Main field of study

  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 19 F,M,T,TkMek for programme students

Autumn 18 F,M,T,TkMek for programme students

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P2 (7.5 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus

    KTH Campus

  • Tutoring time


  • Form of study


  • Number of places *

    Max. 1

    *) If there are more applicants than number of places selection will be made.

  • Course responsible

    Jens Fransson <>

    Luca Brandt <>

  • Teacher

    Jens Fransson <>

    Luca Brandt <>

  • Target group

    For doctoral students at KTH.

Intended learning outcomes

After completing this course the student should manage 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 in oceans and in the atmosphere
  • discuss the non-linear behaviour of water waves
  • 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

Course main content

The student will acquire knowledge in fundamental concepts and phenomena in wave motions in fluids and in 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


To follow the course students (including master students) are required to have taken a course in fluid mechanics.
Compulsory courses of the main programmes at F or T. For F-students SG2223, for T-students SG1217 and for M- and P-students SG1220 are recommended. For M- and P-students 5B1304 is compulsory.


  • Acheson D. J., Elementary Fluid Dynamics, Oxford University Press, USA, 1990 (ISBN 0198596790) / Kundu P. K. and Cohen I M., Fluid Mechanics, Elsevier Academic Press, USA, 2004 (ISBN 0121782530)
  • Your own lecture notes and other distributed course material


  • INL1 - Calculation, 1.5, grading scale: P, F
  • LAB1 - Experiment, 1.5, grading scale: P, F
  • TEN1 - Examination, 4.5, grading scale: A, B, C, D, E, FX, F

Requirements for final grade

Combined oral and written examination (TEN1; 4,5 university credits)
Theoretical home assignment (INL1; 1,5 university credits)
Experimental wind tunnel lab (LAB1; 1,5 university credits)

Offered by



Jens Fransson <>

Luca Brandt <>


Course syllabus valid from: Autumn 2007.
Examination information valid from: Autumn 2007.