| 41223 Linear and Nonlinear Wave Dynamics |
| Danish title: Lineær og ikke-lineær bølgedynamik |
|
Language: English ECTS-creditpoints: 10
|
|
|
Exam schedule:
|
F4-A (jun 04 2002) |
| Scope and form: Lectures, problem sessions and computer exercises |
Evaluation: Oral exam and approval of reports
Weight 50% each |
| Examination: 13-scale |
| Previous course: 04416, 12530, 57345 |
| Prerequisites: Basic knowledge of hydrodynamics and / or fluid dynamics, partial differential equations and Fourier analysis e.g. 12520 / 41311 / 10346 and 01030 / 01032 / 01034. |
| No credit points with: 04416 |
| Aim: To learn basic and advanced theories as well as mathematical formulations and methods with a view to compute linear and nonlinear, regular and irregular water waves on constant and uneven bottom bathymetry. To learn the use of a symbolic mathematical tool to solve these problems |
Contents: Derivation of the governing partial differential equations for the fully nonlinear water wave problem.
Presentation of linear theory for regular waves with emphasis on phenomena such as shoaling, reflection,
refraction and diffraction, and the concepts of group velocity, energy, energy flux and radiation stress.
Presentation of a number of theories for nonlinear regular waves such as Stokes higher order theory, Cnoidal
theory, solitary waves, solitons and streamfunction theory. Introduction to methods for computation of irregular
waves: Different levels of Boussinesq formulations in the time domain, and the corresponding deterministic
equations in the frequency domain. Analysis of frequency dispersion, amplitude dispersion and nonlinear
transfer functions. Introduction to stochastic evolution equations and bispectra. Presentation of advanced
computational methods such as Boundary Integral methods and VOF. Introduction to the symbolic mathematical
tool MATHEMATICA.
The following physical phenomena will be treated in the course: Transformation of regular and irregular waves over varying water depth; nonlinear energy exchange between bound and free waves; modulation and instability of wavetrains in deep water; generation and release of sub- and super-harmonics; low frequency waves in connection with surf beat and harbour resonance; wave breaking and wave induced currents; interaction between waves and ambient currents including Doppler shift and blocking. |
Contact: Per Madsen, building 305, (+45) 4525 3076, prm@imm.dtu.dk
Harry Bingham, building 305, (+45) 4525 3080, hbb@imm.dtu.dk |
| Department: 041 Department of Mechanical Engineering |
| Updated: 22-11-2001 |
|
|
