1.1. Introduction to wave mechanics

Try these first

1. 1.

   What does linear wave theory assume about the nature of waves?

   Hint

   Consider how waves behave in idealized systems.

2. 2.

   What is meant by boundary value problems in fluid mechanics?

   Hint

   Think about situations where solutions depend on limits.

3. 3.

   What is the primary assumption of linear wave theory?

   • Waves are always nonlinear
   • Waves behave linearly under ideal conditions
   • Waves only occur in turbulent flows

   Hint

   Think about when we can simplify complex systems.

4. 4.

   True or False: Kinematic boundary conditions allow fluid to cross an impermeable boundary.

   • True
   • False

   Hint

   Consider the nature of solid boundaries.

5. 5.

   Calculate the wave potential given the following conditions in a fluid channel: width = 3m, velocity = 2m/s, and apply appropriate boundary conditions.

   Hint

   Start with understanding velocity potential derivations and apply continuity.

6. 6.

   Formulate a boundary value problem for a wave moving in a tank where one end is open and the other is closed. What initial conditions should you specify?

   Hint

   Refer to how you define regions and apply flow constraints.