1.2. Linear wave theory

Try these first

1. 1.

   What is the definition of linear wave theory?

   Hint

   Think about the linear characteristics of waves.

2. 2.

   Why are boundary value problems important?

   Hint

   Consider how multiple solutions could arise without constraints.

3. 3.

   What does the linear wave theory primarily analyze?

   • Non-linearity in fluids
   • Linear disturbances in fluids
   • Highly viscous fluids

   Hint

   Think about the assumption of linearity in waves.

4. 4.

   True or False: The Laplace equation can apply to both velocity potential and stream function.

   • True
   • False

   Hint

   Consider the equation's universal application in fluid dynamics.

5. 5.

   Given a wave tank with water height variations, derive the potential flow using boundary conditions based on measured velocity at inlet and outlet.

   Hint

   Define the depths and velocities properly before substituting them into the Laplace equation.

6. 6.

   How would the equations change if the flow is no longer irrotational? Provide new forms for the velocity potentials.

   Hint

   Consider factors like rotational flow and how they relate to velocity potentials.