What Is the Airy Linear Wave Celerity & Dispersion Calculator?
The dispersion relation describes how wave speed depends on wavelength and water depth.
How Does the Airy Linear Wave Celerity & Dispersion Calculator Work?
In deep water (h > L/2), celerity depends only on period; in shallow water (h < L/20), celerity depends only on depth.
Airy Linear Wave Celerity & Dispersion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
\omega^2 = g k \tanh(k h), \quad c = \frac{L}{T} = \frac{g T}{2\pi} \tanh(k h)
Airy transcendental wave dispersion relation.
How to Use the Airy Linear Wave Celerity & Dispersion Calculator
- Input wave period T and water depth h.
Step-by-Step Example Calculation
Continental Shelf Swell
Input Values:
wavePeriodSeconds:10
waterDepthMeters:30
Worked Steps: Predicts wavelength L ~134.6 m, celerity c ~13.5 m/s, classified as intermediate water depth.
Understanding Your Result
Provides wavelength L, phase celerity c, wavenumber k, and water regime classification.
Factors That Affect the Result
- As depth decreases, wave speed and wavelength shrink simultaneously.
When Should You Use This Calculator?
- Coastal breakwater design, harbor layout, and offshore jacket structural wave loading.
Assumptions & Limitations
- Linear Airy wave theory (small wave amplitude relative to wavelength and water depth).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Fenton and McKee explicit formula matches exact roots within 0.1% across all depths.