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{ \Delta \times V = 0 }[/math]

Let:

[math]\displaystyle{ V = \Delta \Phi \to \Delta \times \Delta \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]