What Is the Ocean Wave Dispersion & Celerity Calculator (Airy Theory)?
The linear wave dispersion relation connects wave frequency (ω = 2π/T), wavenumber (k = 2π/L), and water depth (d).
It shows that wave speed (celerity c) depends on both period and depth: longer waves travel faster, and waves slow down as they approach the shore.
How Does the Ocean Wave Dispersion & Celerity Calculator (Airy Theory) Work?
In deep water (d/L > 0.5), tanh(kd) approaches 1.0, so speed depends purely on wave period: c₀ = gT / 2π.
In shallow water (d/L < 0.05), tanh(kd) approaches kd, so speed becomes independent of wave period and depends only on water depth: c = √(gd).
Ocean Wave Dispersion & Celerity Calculator (Airy Theory) Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Implicit linear wave dispersion relation solved iteratively using the Fenton-McKee analytical approximation.
How to Use the Ocean Wave Dispersion & Celerity Calculator (Airy Theory)
- Enter the seabed depth and wave period.
- Check the water depth regime (deep, transitional, shallow).
- Read wave celerity in m/s and knots.
Step-by-Step Example Calculation
10-Second Swell in 50 m Intermediate Depth
Input Values:
Understanding Your Result
As swell shoals into shallow water, wavelength compresses and wave height grows until breaking.
Factors That Affect the Result
- Wave period: Long-period storm swells (T = 15–20 s) travel at over 50 knots across open oceans, outrunning storms.
When Should You Use This Calculator?
- Coastal harbor protection design and wave transformation modeling.
- Calculating water particle kinematics for offshore pile wave loading.
Assumptions & Limitations
- Airy linear wave theory (small wave steepness H/L << 1).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Fenton-McKee approximation is accurate to within ±1.5% of full numerical root-finding.