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Harbor Engineering

Wave Diffraction in Harbors

Real-time K_D distribution via Sommerfeld (Penney-Price) theory for breakwater gaps and semi-infinite barriers. Visualize harbor wave heights and energy flux.

Parameters
Mode
Wave Period T 8.0 s
Water Depth h 15.0 m
Gap Width B 100 m
Incident Angle θ 0 °
0°=normal incidence, ±60°=oblique
Incident Height H₀ 2.0 m
K_D (Harbor Center)
H_harbor [m]
Sheltering [%]
Wave Energy [kW/m]
Steepness H/L
K_D vs Angle (fixed distance)
Centerline H vs Distance

Sommerfeld Diffraction Theory

Diffraction behind a semi-infinite breakwater (Penney-Price):

$$K_D(\xi) = \frac{1}{2}\left|F(\xi_+) + F(\xi_-)\right|$$

Fresnel integral: $F(\xi) = \frac{1+i}{2}\int_\xi^\infty e^{-i\pi t^2/2}dt$

$\xi_\pm = \sqrt{2kr/\pi}\sin[(\theta\pm\alpha)/2]$, wave number $k=2\pi/L$

Wave energy flux: $P = \rho g^2 H^2 T/(32\pi)$ [W/m]

CAE Integration: Boundary conditions and validation for OpenFOAM / MIKE 21 numerical wave modeling. Far-field diffraction coefficient comparison with BEM codes (WAMIT, NEMOH). Preliminary breakwater gap optimization in harbor tranquility studies.