Special Topics on Non-hydrostatic Dynamics

Course ID: D81015E4

Credits: 3

Objective: The object of this course is to introduce the fundamental theory of non-hydrostatic dynamics without the conventional hydrostatic assumption. In particular, non-hydrostatic dynamics plays an important role in the small-scale motions in the atmospheric and ocean environment. Emphasis will be on the theoretical analysis of nonlinear and dispersive fluid motions.

Course Prerequisites: None

Outline: 

1. Dispersion of multi-layer non-hydrostatic free-surface flow 

2. Nonlinearity of multi-layer non-hydrostatic free-surface flow

Teaching Method:  

1. textbook (paper) materials and power-point slides 

2. key derivations on blackboard 

3. different illustrative examples 

4. communication and discussions 

5. homework assignment

Reference:  

1. Fluid Mechanics 

2. Environmental Fluid Mechanics 

3. Water Wave Mechanics for Engineers and Scientists 

4. SCI papers

Course Schedule (subject to change):  

1. Introduction 

2. Governing equations 

3. Continuity and Euler equations 

4. Conventional multi-layer formulation 

5. Integrated multi-layer formulation 

6. Linear wave properties 

7. Dispersion relations 

8. Nonlinear wave properties 

9. Second-order governing equations 

10. Second-order interactions of monochromatic waves 

11. Second-order interactions of bichromatic waves 

* one to two weeks for a topic depending on students’ responses

Evaluation:  

Attendance / Oral presentations (30%) 

Homework Assignments (20%)

Midterm Exam (20%)

Term Project (30%)