Waves advancing into shallow water

Question 1

What defines a wave form for shallow water analysis?

Answer 1

(i) Wave period T
(ii) Wave-length λ
(iii) Wave amplitude a

Question 2

True or False: Wave amplitude and wave-length remain constant in shallow water.

Answer 2

False – only wave period remains constant; wave amplitude and wave-length change.

Question 3

State the two key assumptions made for waves advancing into shallow water.

Answer 3

(A) Water depth varies slowly → previous wave equations apply
(B) No energy losses (ignore friction)

Question 4

True or False: The dispersion equation can be solved explicitly for k.

Answer 4

False – it must be solved iteratively or graphically.

Question 5

Write the Energy Conservation Equation [3a] for wave shoaling.

Answer 5

1/2gρcga^2 = constant

Question 6

Final equation showing change in wave height from deep to shallow water using energy conservation?

Answer 6

a = a₀ · √(c_g0 / c_g)

Question 7

Why does wave amplitude increase in shallow water?

Answer 7

Because group velocity cg decreases, and energy conservation requires that wave height a increases to maintain constant energy flux.