| Recommended semester: 7th - 9th semester |
| Scope and form: Lectures and exercises |
| Evaluation: Approval of coursework/reports
|
| Examination: 13-scale |
| Prerequisites: Elementary knowledge of hydrodynamics or fluid mechanics. Experience with partial differential eauations and Fourier analysis. |
Aim: The course, consisting of lectures and problem sessions, will include
theoretical and mathematical formulations and numerical methods with a view to compute nonlinear irregular water waves and their interaction with fixed and floating structures. The symbolic modelling tool MATHEMATICA will be introduced and applied throughout the course. |
Contents: With a starting point in the basic hydrodynamic equations, a number of
mathematical and theoretical formulations for non-linear water waves will be derived and analysed. The basic theories for linear and nonlinear regular waves will be reviewed including Stokes' first, second and third order theory and stream function theory. Methods for calculating irregular waves will concentrate on: Various levels of Boussinesq equations formulated in the time domain; the corresponding deterministic evolution equations in the frequency domain; and an introduction to the concept of stochastic evolution equations and bispectra. The various formulations will be analyzed with respect to frequency-dispersion, amplitude-dispersion and non-linear transfer functions. The linear wave-body interaction problem will be derived, and an introduction given to the solution via a panel method. An introduction is also provided to a direct numerical solution of the Euler equations with emphasis on methods for handling moving boundaries (Marker-and-Cell, Volume-Of-Fluid, Level Set, Adaptive net).
The following physical phenomena will be treated: Transformation of irregular waves over varying water depth; energy exchange between bound and free waves; generation and release of sub- and super-harmonic waves; low frequency waves in connection with surf beat and harbour resonance; wave breaking and generation of wave-driven currents; interaction between waves and currents including Doppler shift and wave blocking; interaction between waves and fixed / floating structures (e.g. moored ships). |
Contact: Per Madsen, building 305, (+45) 4525 3076, prm@imm.dtu.dk
Harry Bingham, building 305, (+45) 4525 3080, hbb@imm.dtu.dk |
| Department: 002 Informatics and Mathematical Modelling |
| Course URL: http://www.imm.dtu.dk/courses/02615 |
| Keywords: Nonlinear irregular waves, Wave-body interaction, Boussinesq equations, Mathematical programming |
| Updated: 11-01-2002 |
