Conservation Laws and Boundary Conditions

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:

[math]\displaystyle{ \nabla \times \overrightarrow{V} = 0 }[/math]

Let:

[math]\displaystyle{ \overrightarrow{V} = \nabla \Phi \to \nabla \times \nabla \Phi = 0 }[/math]

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]