Second-order effects Flashcards
What are the two types of wave energy?
- Potential energy – due to the position of fluid particles
- Kinetic energy – due to the motion of fluid particles
What is the formula for wave potential energy relative to still water?
PE_waves = PE_total - PE_still water
In the formula “PE = mgh”, the variable h is replaced by ƞ +d, where ƞ is _____ and d is _______.
wave surface elevation, water depth
What is the expression for Potential Energy per unit area of a wave?
PE_waves = (1/λ) ∫[x₀ to x₀+λ] [ (1/2)ρg(η + d)² − (1/2)ρgd² ] dx
What does the integration of sin(ωt − kx) over one wavelength equal?
∫[x₀ to x₀ + λ] sin(ωt − kx) dx = 0
What is the final expression for average potential energy per unit area of a wave?
PE_waves = (1/4)ρga²
What is the total energy per unit area of a wave (potential + kinetic)?
E_waves = PE_waves + KE_waves = (1/2)ρga²
What is group velocity cg in wave theory?
The velocity at which energy or information propagates through a wave train — not the same as phase velocity.
In deep water, energy propagates at __________ the phase speed.
half
What is the general expression for group velocity cg?
c_g = dω/dk
Final form of group velocity in terms of c.
c_g = (1/2)·c·[1 + (2kd) / sinh(2kd)]
Match the water depth condition with its group velocity rule:
- Deep Water:
- Shallow Water:
- cg = 1/2c
- cg = c
True or False: In shallow water, group velocity equals phase velocity.
True
