Difference between revisions of "Conservation Laws and Boundary Conditions"
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The Ocean Environment | The Ocean Environment | ||
| − | + | Non Linear Free-surface Condition | |
| − | (X,Y,Z): | + | (X,Y,Z): Earth Fixed Coordinate System |
| − | X: | + | X: Fixed Eulerian Vector |
| − | v: | + | v: Flow Velocity Vector At X |
| − | : | + | : Free Surface Elevation |
Assume ideal fluid (No shear stresses) and irrotational flow: | Assume ideal fluid (No shear stresses) and irrotational flow: | ||
| − | <center><math>\ | + | <center><math>\nabla \times \overrightarrow{V} = 0</math></center> |
Let: | Let: | ||
| − | <center><math>V = \ | + | <center><math> \overrightarrow{V} = \nabla \Phi \to \nabla \times \nabla \Phi = 0 </math></center> |
Where <math>\Phi(X,t) is the velocity potential assumed sufficiently continuously differentiable. | Where <math>\Phi(X,t) is the velocity potential assumed sufficiently continuously differentiable. | ||
Revision as of 11:16, 16 January 2007
The Ocean Environment
Non Linear Free-surface Condition
(X,Y,Z): Earth Fixed Coordinate System X: Fixed Eulerian Vector v: Flow Velocity Vector At X
- Free Surface Elevation
Assume ideal fluid (No shear stresses) and irrotational flow:
Let:
Where [math]\displaystyle{ \Phi(X,t) is the velocity potential assumed sufficiently continuously differentiable. Potential flow model of surface wave propagation and wave-body interactions very accurate. Few important exceptions will be noted. Conservation of mass: \lt center\gt \lt math\gt \Delta \dot V = 0 }[/math]
