The University of Southampton

SESS3023 Marine Hydrodynamics

Module Overview

This module will develop the fundamentals of fluid mechanics in the context of naval architecture and ocean engineering. The module continues from the more descriptive fluid mechanics material in part 1 and part 2, and develops the mathematical, computational, and conceptual techniques needed to solve for the flow around ship shaped bodies and lifting surfaces. These concepts will have direct relevance to other modules in part 3 and part 4 modules where evaluation of added mass, boundary layers, and numerical methods are necessary to establish the fluid loading and motion of maritime structures and vessels. The effects of a free surface are not included in the module.

Aims and Objectives

Module Aims

• Provide a basic understanding of the mechanisms involved in two-dimensional boundary layer flow. • Introduce the concepts of two-dimensional complex potential flow methods to infinite flow domains. • Introduce the concepts of conformal mappings and their uses in two-dimensional flow problems. • To introduce panel methods and boundary layer integral methods in preparation for CFD applications.

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • The governing equations of motion for boundary layers from the Navier-Stokes equation.
  • The effects of differing boundary layer profiles.
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • Develop the methodology for the estimates of skin friction estimates.
  • Introduce the concepts of complex potential definition of basic flow regimes
Transferable and Generic Skills

Having successfully completed this module you will be able to:

  • Understand basic methods of analysis of engineering problems with fluid interaction.
Subject Specific Practical Skills

Having successfully completed this module you will be able to:

  • Use conformal mapping techniques and panel methods to investigate the flow around noncircular bodies.
Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

  • Basic Mathematical Skills: Basic complex variable revision. Introduction to Cauchy Integral methods and boundary integrals. Identification of poles and zero's.
  • Complex Potential: Definition of w, the complex potential, in terms of velocity potential and the stream function. Derivation of total velocity from w. Fundamental hydrodynamic sources: source, sink, vortex, dipole and free stream.
  • Mapping Techniques:Mapping functions and their uses is explored to transform complex shapes to circles and straight lines. Addition of vorticity for reality in flow. Determination of lift and drag and lines of action.
  • Boundary Layer Methods:Development of Navier Stokes methods and Prandtl equivalents. Simplified boundary layer profiles, estimation of skin friction values, dependence upon Reynolds Number. Momentum integral equation
  • Numerical Methods for Potential Flows:Develop equations for a vortex panel and solve a system of equations describing the superposition of panels to determine the flow around any two-dimensional body. Enforce the numerical Kutta condition and determine the lift. Development numerical integration of general boundary layer flows with pressure gradients. Link the panel method and integral method to determine flow separation and forces.


The module will develop the ideas of the previous fluid dynamics modules from Part 1 and Part 2 modules. The main ideas will be conveyed using complex variable theory for potential flow conditions. The module oversees the theory behind the estimation of lift and drag on wings, ships, etc. The second part of the module addresses the boundary layer problem using conventional techniques for laminar and turbulent flow. The third part of the module introduces the ideas behind Computational Fluid Dynamics (CFD).

Learning and Teaching

Teaching and learning methods

Teaching methods include • Lecturing the course using examples from real ship situations as examples of where the techniques apply. • 3 weeks in the design studio developing and applying a numerical flow solver. Learning activities include • Understanding the mathematical techniques of complex variables. • Understanding by performing examples of the lift and drag from Joukowski aerofoils.

Wider reading or practice22
Supervised time in studio/workshop9
Completion of assessment task12
Follow-up work10
Preparation for scheduled sessions10
Total study time150

Resources & Reading list

James. Modern Engineering Mathematics. 

Theoretical Hydrodynamics. 

Blackboard. The blackboard web site has links to a number of websites that have demonstrations of how the transforms work and show how the streamlines are modified.

Lamb. Hydrodynamics. 

Mechanics of Fluids. 

Jupyter notebooks for the numerical methods sections.



MethodPercentage contribution
Coursework assignment(s) 10%
Coursework assignment(s) 10%
Coursework assignment(s) 10%
Exam  (120 minutes) 70%


MethodPercentage contribution
Exam  (120 minutes) 100%

Repeat Information

Repeat type: Internal & External

Linked modules


To study this module, you will need to have studied the following module(s):

SESS2018Ship Powering and Control Surfaces
SESS2015Hydrodynamics and Seakeeping
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