Harbor Tsunami Defense: Shallow-Water Shoaling & Breakwater Transmission (2D)

Incoming Wave

Offshore wave height (H₀) 2.0 m

Wave period (T) 60 s

Shelf & Harbor Depth

Shelf depth (h₁) 40 m

Harbor basin depth (h₂) 5.0 m

Breakwater at Harbor Mouth

Crest freeboard (Rc) 1.5 m

Gap width open 15%

Live Readout

c offshore (√gh₁)

0.0 m/s

c in harbor (√gh₂)

0.0 m/s

Green's-law shoal ×

0.0×

Transmission Kt

0.00

Max height, harbor mouth

0.0 m

Max runup, quay wall

0.0 m

How it works

A leapfrog (Arakawa C-grid) finite-difference solver marches the 1D linear shallow-water equations along a real shelf→harbor depth cross-section h(x):

∂u/∂t = −g·∂η/∂x − r·u
∂η/∂t = −∂(h·u)/∂x
c(x)  = √(g·h(x))        (shallow-water wave speed)

Because c falls as the profile shoals, wave energy flux (∝ c·H²) is conserved by raising H — the classic Green's-law shoaling relation H ∝ h⁻¹ᐟ⁴, shown live against the measured height at the harbor mouth. The breakwater applies a relative-freeboard transmission coefficient Kt (standard coastal-engineering practice: Kt falls as crest freeboard Rc grows relative to incident height H₀, and rises toward 1 for a submerged/negative-freeboard structure), blended with the open-gap fraction left un-armoured. Kt scales the flow crossing the harbor mouth each step — energy that isn't transmitted reflects back offshore, exactly like a real partial breakwater.

Left boundary — a wavemaker forcing η(0,t)=H₀·sin(ωt), radiating a real wave train shoreward.
Right boundary — the harbor quay: a solid wall (u=0) whose peak η is the flooding/runup readout.
Breakwater — sits at the harbor mouth; its Kt is recomputed live from freeboard and gap-width so every slider visibly changes both the shoaling curve and the flooding outcome.

Water surface η(x) Sea/harbor floor h(x) Breakwater