1. What is Wave Celerity in Shallow Water?

Wave celerity in shallow water refers to the speed at which waves propagate through water depths where the effects of the seabed are significant. In shallow water conditions, wave speed becomes dependent on water depth rather than wave period.

2. How Does the Calculator Work?

The calculator uses the shallow water wave celerity formula:

Where:

• \( C_s \) — Wave celerity for shallow depth (m/s)
• \( g \) — Gravitational acceleration (9.80665 m/s²)
• \( d_s \) — Shallow depth (m)

Explanation: This formula demonstrates that in shallow water conditions, wave speed is proportional to the square root of water depth, making it independent of wave period.

3. Importance of Wave Celerity Calculation

Details: Accurate wave celerity calculation is crucial for coastal engineering, navigation safety, sediment transport studies, and understanding wave transformation in nearshore environments.

4. Using the Calculator

Tips: Enter the shallow water depth in meters. The value must be positive and represents the vertical distance from the water surface to the seabed.

5. Frequently Asked Questions (FAQ)

Q1: What defines "shallow water" for wave propagation?
A: Water is considered shallow for wave propagation when the depth is less than 1/20 of the wavelength (d < L/20).

Q2: How does wave celerity change from deep to shallow water?
A: In deep water, wave celerity depends on wave period. In shallow water, it depends only on water depth and decreases as depth decreases.

Q3: What are typical wave celerity values in shallow water?
A: Typical values range from 1-10 m/s depending on water depth, with shallower depths producing slower wave speeds.

Q4: Are there limitations to this formula?
A: This formula applies only to non-breaking waves in shallow water conditions and assumes uniform depth and small amplitude waves.

Q5: How is this calculation used in practical applications?
A: It's used in coastal engineering for breakwater design, in navigation for predicting wave arrival times, and in environmental studies of coastal processes.