Model nearshore wave growth from decreasing depth accurately. Compare coefficients, celerity, and group velocity instantly. Built for coastal planning, harbor studies, and design reviews.
| Case | H0 (m) | T (s) | h (m) | Angle (deg) | Approx. Ks | Approx. H (m) |
|---|---|---|---|---|---|---|
| Harbor approach | 1.20 | 8.00 | 6.00 | 10 | 1.14 | 1.37 |
| Beach profile review | 1.80 | 10.00 | 8.00 | 15 | 1.19 | 2.14 |
| Breakwater screening | 2.30 | 12.00 | 10.00 | 5 | 1.21 | 2.79 |
These rows are sample planning values for demonstration only.
Deepwater wavelength: L0 = gT² / 2π
Dispersion equation: ω² = gk tanh(kh)
Local wavelength: L = 2π / k
Phase speed: C = L / T
Group factor: n = 0.5[1 + (2kh / sinh(2kh))]
Group speed: Cg = nC
Shoaling coefficient: Ks = √(Cg0 / Cg)
Snell relation: sin(α) / C = sin(α0) / C0
Refraction coefficient: Kr = √(cos α0 / cos α)
Transformed wave height: H = H0 × Ks × Kr
Wave energy density: E = (1/8)ρgH²
Simple depth-limited check: Hmax ≈ 0.78h
A wave shoaling calculator helps engineers estimate how waves change as water becomes shallower. This process matters near beaches, harbors, seawalls, revetments, and offshore approach channels. When depth decreases, wave speed drops. Wavelength shortens. Energy is compressed into a smaller zone. Wave height often increases before breaking begins. These changes affect overtopping, sediment transport, structural loading, and navigation safety. Reliable shoaling estimates support stronger coastal layouts and better risk reviews.
Wave transformation is not only about height. Engineers also track celerity, group velocity, energy density, and energy flux. These values shape armor sizing, crest elevation checks, scour predictions, and shoreline response studies. A good calculator lets designers compare deepwater conditions with local depth conditions quickly. That saves time during concept design, detailed analysis, and report preparation. It also reduces hand calculation errors when several sea states must be reviewed.
This tool uses linear wave theory and the dispersion relationship. It solves wave number iteratively, then computes wavelength, phase speed, and group speed at the selected depth. After that, it estimates the shoaling coefficient. If a deepwater wave angle is entered, it also applies a refraction factor based on Snell’s law. The final outputs include transformed wave height, local wave angle, steepness, and a simple breaking check. These results are practical for coastal screening studies.
Wave shoaling results should be interpreted with engineering judgment. Depth changes, bottom slope, currents, diffraction, and nonlinear effects can alter field behavior. Very steep waves may break before reaching the selected point. Complex bathymetry may require spectral or numerical models. Still, this calculator is useful for first-pass design, classroom work, tender notes, and method statements. It provides fast visibility into nearshore wave growth and coastal energy patterns.
Use consistent units for height, depth, and density. Enter realistic wave periods from measured data or site criteria. Keep approach angles below ninety degrees. Review outputs with local bathymetry and breaking limits. For critical projects, validate these estimates against trusted coastal manuals or advanced modeling tools. That approach turns a fast calculator into a dependable engineering decision aid.
Wave shoaling is the increase in wave height that often occurs as waves move into shallower water. Reduced depth changes speed, wavelength, and energy distribution. That transformation is important in coastal engineering, harbor design, and shoreline protection studies.
The shoaling coefficient, Ks, measures how wave height changes due to depth alone under linear wave theory. A value above one means the wave height increases as depth decreases, assuming other influences remain controlled.
Wave period controls wavelength, celerity, and group velocity. Longer periods usually interact with depth differently than shorter periods. That makes the period essential when estimating local wave transformation and coastal energy transport.
Enter a deepwater angle when you want to include refraction effects. Refraction changes the local approach angle and can raise or lower the transformed height depending on geometry. Use zero when angle effects are not needed.
No. The 0.78h check is a simple screening rule. Real breaking depends on slope, currents, wave spectrum, irregularity, and bottom shape. Use it for quick review, not as the only design criterion.
No. It is best for first-pass evaluation, teaching, and design screening. Projects with complex bathymetry, diffraction, strong currents, or irregular wave climates usually need spectral or numerical modeling for detailed decisions.
Use consistent engineering units throughout the calculation. Heights and depths should use the same length unit. Density and gravity should match the chosen system. The default values are set for common metric coastal engineering work.
It is useful for beach studies, harbor approaches, breakwater screening, revetment checks, classroom problems, and coastal concept design. It quickly shows how depth changes can alter nearshore wave height and energy conditions.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.