Educational paraxial scalar diffraction model: uniform depth, monochromatic waves and ideal screens. It does not compute harbour reflection, breaking, bottom friction, bathymetry, directional spectra or vessel motion. Do not use it to assess harbour tranquillity or safety.
Parameters
s
m
°
m
m
m
m
Results
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Amplitude ratio K_D
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Probe wave height H
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Wavelength L
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Group speed C_g
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Incident flux P₀
Fresnel amplitude map
Yellow dot: probe. Dashed line: paraxial incident direction. Colour indicates amplitude ratio K_D (blue: small; red: 1 or above); brightness oscillations indicate phase. Metre-based coordinates and results do not depend on screen width.
Theory & Key Formulas
Educational paraxial scalar diffraction model: uniform depth, monochromatic waves and ideal screens. It does not compute harbour reflection, breaking, bottom friction, bathymetry, directional spectra or vessel motion. Do not use it to assess harbour tranquillity or safety.
The edge opens toward y>0; the aperture spans −B/2<y<B/2. With paraxial incident slope p=sinθ, use Y=y−xp. For the aperture, u±=(±B/2−Y)√(2/(Lx)), F=C+iS and K_D=|F(u+)−F(u−)|/√2. This is not the Penney–Price solution with reflecting water-wave boundaries.
Finite-depth group speed is obtained by differentiating the dispersion relation. In shallow water C_g≈√(gd); in deep water C_g≈C/2. Incident mean energy density uses wave height H₀, not amplitude: ρgH₀²/8. Multiply by C_g for flux. Constants: ρ=1025kg/m³, g=9.81m/s².
Reading the results
🙋
If wave height halves, does energy halve too?
🎓
At the same depth, linear-wave energy density scales with height squared: K_D=0.5 gives one quarter. P₀ on this page is incident flux, not an energy balance for an entire harbour.
🙋
Does K_D above 1 mean a calculation error?
🎓
Not necessarily. Diffraction and interference can locally amplify a wave. Compare locations rather than clipping K_D to 1. This does not certify safety.
Load a reproducible example
The shadow-edge example uses θ=0°, y=0m: K_D=0.500 and H=0.500m for H₀=1m. The shallow example uses T=18s, d=3m: L≈97.042m. The aperture example uses T=6s, d=10m, B=50m, x=300m and y=0m. Interference makes aperture response non-monotonic in width and position.
Theory & Key Formulas
Educational paraxial scalar diffraction model: uniform depth, monochromatic waves and ideal screens. It does not compute harbour reflection, breaking, bottom friction, bathymetry, directional spectra or vessel motion. Do not use it to assess harbour tranquillity or safety.
The edge opens toward y>0; the aperture spans −B/2<y<B/2. With paraxial incident slope p=sinθ, use Y=y−xp. For the aperture, u±=(±B/2−Y)√(2/(Lx)), F=C+iS and K_D=|F(u+)−F(u−)|/√2. This is not the Penney–Price solution with reflecting water-wave boundaries.
Finite-depth group speed is obtained by differentiating the dispersion relation. In shallow water C_g≈√(gd); in deep water C_g≈C/2. Incident mean energy density uses wave height H₀, not amplitude: ρgH₀²/8. Multiply by C_g for flux. Constants: ρ=1025kg/m³, g=9.81m/s².
Frequently asked questions
Can I use this for harbour design?
No. It combines linear-wave dispersion with an educational Fresnel approximation. It does not model real harbour reflection or breaking and cannot assess safety or mooring conditions.
Is K_D above 1 an error?
Local interference can produce an amplitude ratio above 1. It does not mean that the total energy across a harbour has increased.
Can depth and period be chosen independently?
Yes. Specifying uniform depth d and period T determines k and L through ω²=gk tanh(kd). It does not make T and d dependent on each other.
What does the energy flux represent?
P₀=(ρgH₀²/8)C_g is the incident regular-wave flux in kW/m. It is not an irregular-wave significant-height, local wave-force or overtopping prediction.
