1. What is the Shoaling Coefficient?

The Shoaling Coefficient is a dimensionless parameter used in the study of wave dynamics, particularly in shallow water wave theory. It quantifies how wave height changes as waves propagate into shallower water due to shoaling effects.

2. How Does the Calculator Work?

The calculator uses the shoaling coefficient formula:

Where:

• \( K_s \) — Shoaling Coefficient (dimensionless)
• \( k \) — Wave Number for Water Wave (rad/m)
• \( d \) — Coastal Mean Depth (m)
• \( \tanh \) — Hyperbolic tangent function
• \( \sinh \) — Hyperbolic sine function

Explanation: The formula accounts for how wave characteristics change as waves move from deep to shallow water, incorporating both hyperbolic tangent and sine functions to model the wave transformation process.

3. Importance of Shoaling Coefficient

Details: The shoaling coefficient is crucial for coastal engineering, wave energy prediction, and understanding how wave height increases as waves approach the shore. It helps in predicting wave behavior in transitional water depths between deep and shallow water conditions.

4. Using the Calculator

Tips: Enter the wave number (k) in radians per meter and coastal mean depth (d) in meters. Both values must be positive numbers. The calculator will compute the shoaling coefficient using the standard formula.

5. Frequently Asked Questions (FAQ)

Q1: What is wave number (k) in wave dynamics?
A: Wave number represents the spatial frequency of a wave, indicating how many wavelengths occur in a given distance. It is defined as \( k = \frac{2\pi}{\lambda} \), where λ is the wavelength.

Q2: How does water depth affect wave shoaling?
A: As waves move into shallower water, their speed decreases, wavelength shortens, and wave height increases due to conservation of energy, which is quantified by the shoaling coefficient.

Q3: What is the range of typical shoaling coefficient values?
A: Shoaling coefficient typically ranges from about 0.8 to 1.3, with values greater than 1 indicating wave height amplification and values less than 1 indicating wave height reduction.

Q4: How is this different from refraction coefficient?
A: While both affect wave height, shoaling coefficient accounts for depth-induced changes in wave characteristics, while refraction coefficient accounts for wave direction changes due to depth variations.

Q5: When is the shoaling effect most significant?
A: Shoaling effects are most pronounced when waves transition from intermediate to shallow water depths, typically when the water depth is less than half the wavelength.