1.7. Dispersion Relationship

Try these first

1. 1.

   What is Velocity Potential in fluid mechanics?

   Hint

   Think about scalar functions and fluid equations.

2. 2.

   What happens to water particle displacement in shallow water?

   Hint

   Consider how depth influences the shape of the orbit.

3. 3.

   What does the velocity potential describe?

   • Flow velocity in a fluid
   • Pressure of a fluid
   • Density of a fluid

   Hint

   Think about what controls the motion in fluids.

4. 4.

   True or False: In shallow water, particle paths are circular.

   • True
   • False

   Hint

   Consider how depth changes affect shapes.

5. 5.

   Given a specific wave height and wavelength, derive the equations for D and B in both shallow and deep water conditions and discuss how these parameters reflect wave behavior.

   Hint

   Analyze how depth affects these relationships.

6. 6.

   Using computational tools, demonstrate the calculation of kd through the equation kd² = y² + y/(1 + Σ from n=1 to n=6 of dn * Y_n. Explain how this aids in practical scenarios.

   Hint

   What values can vary to observe changes in results?