Search course

Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
TME225 - Mechanics of fluids
Syllabus adopted 2014-02-20 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mechanical Engineering
Department: 42 - APPLIED MECHANICS

Teaching language: English
Open for exchange students
Block schedule: B

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0111 Examination 7,5 c Grading: TH   7,5 c   30 Oct 2014 am M,  05 Jan 2015 pm M,  25 Aug 2015 am M

In programs



Professor  Lars Davidson

Course evaluation:

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

A basic course in fluid mechanics


The course provides an introduction to continuum mechanics and turbulent fluid flow.

Learning outcomes (after completion of the course the student should be able to)

  • Confidently manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.

  • Derive the Navier-Stokes equations and the energy equation using tensor notation

  • Analytically solve Navier-Stokes equations for a couple of simple fluid flow problems and analyze and understand these flows

  • Characterize turbulence

  • Understand and explain the energy spectrum for turbulence and the cascade process

  • Derive the exact transport equations for the turbulence kinetic energy and the turbulent Reynolds stresses

  • Identify the various terms in these equations and describe what role they play

  • Derive the linear velocity law and the logarithmic velocity law for a turbulent boundary layer



    The students will initially learn the basics of Cartesian tensors and the index notation.

    A strong focus is placed on deriving and understanding the transport
    equations in three dimensions.These equations provide a generic basis
    for fluid mechanics, turbulence and heat transport. In continuum
    mechanics we will discuss the strain-rate tensor, the vorticity tensor
    and the vorticity vector. In connection to vorticity, the concept of
    irrotational flow, inviscid flow and potential flow will be introduced.
    The transport equation for the vorticity vector will be derived from
    Navier-Stokes equations.

    Developing channel flow will be analyzed in detail. The results from a
    numerical solution is provided to the students. In a Matlab assignment,
    the students will compute different quantities such as the increase in
    the centerline velocity, the decrease of the wall shear stress, the
    vorticity, the strain-rate tensor, the dissipation, the eigenvectors and
    the eigenvalues of the strain-rate tensor.

    In the larger part of the course the students will learn the basics of
    turbulent flow. Turbulence includes short-lived eddies of different size
    and frequency. The larger the Reynolds number, the larger the
    difference in size and frequency between the largest and the smallest
    eddies. This is the very reason why there is no computer large enough at
    which we can numerically solve the Navier-Stokes equations at high
    Reynolds number.

    The energy spectra and the energy cascade process will be discussed in
    some detail; in the energy cascade it is assumed that turbulent kinetic
    energy is transferred from the largest energy-rich turbulent eddies to
    the smallest eddies. At the small eddies the kinetic energy is
    transformed into internal energy, i.e. an increase in temperature.

    From the instantaneous Navier-Stokes equations the time averaged
    momentum equation will be derived. In this equation appears a new term,
    the turbulent Reynolds stress tensor. The students will learn how to
    derive the exact Reynolds stress transport (RST) equation, as well as
    the equations for turbulent kinetic energy and mean kinetic energy. The
    physical meaning of the different terms in the RST equation, such as the
    production term, the pressure-strain term and the dissipation, will be
    discussed in some detail.

    In a second Matlab assignment, the students will be given a database of
    instantaneous turbulent flow for fully developed channel flow. The
    students will compute and analyze various turbulent quantities such as
    the turbulent Reynolds stresses, the pressure strain term in the RST
    equation, the two-point correlation, the integral turbulent length scale
    and the dissipation.

    .For more information

    .Lecturer's homepage


    Lectures, workshops using Matlab, assignments including written reports


    Lecture notes which can be downloaded from the course web page


    Assignments and written examination

    Page manager Published: Thu 04 Feb 2021.