What Is the Green’s Law Wave Shoaling & Amplitude Calculator?
Green’s Law describes the energy conservation of non-breaking long waves in slowly varying shallow channels.
How Does the Green’s Law Wave Shoaling & Amplitude Calculator Work?
As water depth decreases, wave propagation celerity c = sqrt(g*h) slows down, compressing wave energy into greater height.
Green’s Law Wave Shoaling & Amplitude Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
H_2 = H_1 \left( \frac{b_1}{b_2} \right)^{1/2} \left( \frac{h_1}{h_2} \right)^{1/4}, \quad c = \sqrt{g h}
Green’s law for long wave amplitude shoaling and shallow water wave celerity.
How to Use the Green’s Law Wave Shoaling & Amplitude Calculator
- Input initial wave height, initial and shallow water depths, and channel widths.
Step-by-Step Example Calculation
Tsunami Coastal Shoaling
Input Values:
initialWaveHeightMeters:1
initialWaterDepthMeters:50
shoaledWaterDepthMeters:5
initialChannelWidthMeters:1
shoaledChannelWidthMeters:1
Worked Steps: Predicts shoaling amplification factor of 1.778× and shoaled wave height of 1.78 m.
Understanding Your Result
Reveals shoaled wave height, amplification factor, and wave speeds.
Factors That Affect the Result
- Channel funneling (b1 > b2) compounds with depth reduction to create extreme wave run-up heights.
When Should You Use This Calculator?
- Tsunami inundation hazard forecasting, tidal bore modeling, and harbor basin resonance analysis.
Assumptions & Limitations
- Assumes long shallow water waves (wavelength L >> depth h) with negligible bottom friction and no wave breaking.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical hydrodynamics formulation first derived by George Green in 1837.