TVM0024, Viscous flow (SE: Viskös strömning), 12 ECTS

COURSE SYLLABUS, third-cycle courses

Course name: Viscous flow (SE: Viskös strömning)

ECTS: 12 ECTS

Course Code: TVM0024

Educational level: Third-cycle course

Entry requirements: Admitted to PhD studies at TVM

Implementation

The course will be in the form of seminars where you make presentations of the contents. Solutions to problems should be presented. The presentations and solutions are discussed in plenum with senior staff from Fluid Mechanics. Demos should be carried out.

Learning outcomes

You should master the theory and physics of viscous flow and understand the strength and weaknesses of analytical modelling. You should also be equipped with a pallet of methods that can be used to solve problems within fluid dynamics as well as having knowledge of a relatively large number of cases that can be solved with these methods and be ready to break-down complex fluid mechanical problems into generic cases, solve them and draw conclusions on the complex problem from the results. You shall also be able to relate the content in the course to the own research.

Course content

(following the Chapters in Kundu):

1. Introduction

1. Fluid mechanics (Kundu 1.1-1.3)
2. Continuum approximation (Kundu 1.4-1.5)
3. Surface tension and Fluid Statics (Kundu 1.6-1.7)
4. Thermodynamics (Kundu1.8-1.9)
5. Stability (Kundu 1.10)

1. Laminar flow

1. Exact solutions (Kundu 9.1-9.2)
2. Elementary lubrication theory (Kundu 9.3)
3. Similarity solutions for unsteady incompressible viscous flow (Kundu 9.4)
4. Flows with oscillations (Kundu 9.5)
5. Low Reynolds number flow past sphere until Oseen’s solution (Kundu 9.6)
6. Low Reynolds number flow past sphere: Oseen’s solution (Kundu 9.6)

1. Vorticity

1. Introduction (5.1).

1. Kelvin’s and Helmholtz’s theorems (5.2)
2. Vorticity equation in a nonrotating frame (5.3), meaning of the term ωjui,j (small part of 5.5).
3. Velocity induced by a vortex filament: law of Biot and Savart (5.4), Vortex sheet (5.7)
4. Vorticity equation in a rotating frame of reference (5.5)
5. Interaction of vortices (5.6)

1. Boundary layers and related topics

1. Derivation of boundary layer equation and thicknesses (Kundu 10.1-10.2)
2. Blasius solution (Kundu 10.3)
3. Transition, pressure gradient and boundary layer separation (Kundu 10.7)
4. Flow past circular cylinder (Kundu 10.8)
5. Flow past a sphere (Kundu 10.9)
6. Two-dimensional jets (Kundu 10.10)
7. Secondary flows (Kundu 10.11)

1. Instability: Everybody must read 11.1-11.2 to understand the upcoming discussion

1. Kelvin Helmholtz instability (Kundu 11.3)
2. Thermal instability (Kundu 11.4)
3. Double-Diffusive instability, Centrifugal instability (Kundu 11.5-6)
4. Instability of continuously stratified parallel flows (Kundu 11.7)
5. Squires theorem and Orr-Sommerfeld, Inviscid stability (Kundu 11.8-11.9)
6. Nonlinear effects (Kundu 11.12-11.14)

1. 13.1-13.5
2. 13.6-13.13
3. 13.14-13.16

1. 14.1-14.4
2. 14.5-14.7
3. 14.8-14.9

Examination

You are judged from the presentations of the literature content at each seminar including homework problems as well as how active you are in the discussions.

Grading scale: Pass/Fail.

Course literature: Kundu, Fluid Mechanics, Sixth Edition, P.K. Kundu. I.M. Cohen, D.R. Dowling, ISBN-978-0-12-405935-1

Education cycle: September 2026 – December 2026

Course is given periodically: No.

Send application to: Prof. Staffan Lundström, stlu@ltu.se. Doctoral student enter name, civic registration number, e-mail, Division and Department in the application.

Deadline for application

2026-09-01

Course open for application by doctoral students admitted to other universities than LTU: No

Limited number of students: 30

Tuition

No tuition fee.

Contact persons and teachers: Prof. Staffan Lundström, e-mail: stlu@ltu.se, phone: +46 920 492392 | Dr. Joel Sundström: joel.sundstrom@ltu.se

Examiner: Prof. Staffan Lundström, e-mail: stlu@ltu.se, phone: +46 920 492392.

Course syllabus decided by: Prof. Lars-Göran Westerberg, director for PhD studies

Date of decision: 2026-08-12