Breaker Depth Index Given Set-down At Breaker Point At Still-water Shoreline Calculator

Breaker Depth Index Formula:

\[ \gamma_b = \sqrt{\frac{8}{3} \times \left( \frac{d_b}{\eta_s - \eta_b} - 1 \right)} \]

Water Depth at Breaking (d_b):

Setup at the Still-Water Shore Line (η_s):

Set Down at the Breaker Point (η_b):

Breaker Depth Index (γ_b):

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1. What is the Breaker Depth Index?

The Breaker Depth Index is the ratio of the wave height at breaking to the water depth at the breakpoint. It's a crucial parameter in coastal engineering that helps predict wave breaking characteristics and their impact on shorelines.

2. How Does the Calculator Work?

The calculator uses the Breaker Depth Index formula:

\[ \gamma_b = \sqrt{\frac{8}{3} \times \left( \frac{d_b}{\eta_s - \eta_b} - 1 \right)} \]

Where:

\( \gamma_b \) — Breaker Depth Index
\( d_b \) — Water Depth at Breaking (m)
\( \eta_s \) — Setup at the Still-Water Shore Line (m)
\( \eta_b \) — Set Down at the Breaker Point (m)

Explanation: This formula calculates the breaker depth index by considering the relationship between water depth at breaking and the difference between setup at the still-water shoreline and set down at the breaker point.

3. Importance of Breaker Depth Index Calculation

Details: Accurate calculation of breaker depth index is essential for coastal engineering projects, shoreline management, and predicting wave behavior near coastlines. It helps in designing coastal structures and understanding sediment transport processes.

4. Using the Calculator

Tips: Enter water depth at breaking, setup at the still-water shore line, and set down at the breaker point in meters. All values must be valid positive numbers, and setup must be greater than set down.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for Breaker Depth Index?
A: The breaker depth index typically ranges from 0.6 to 1.2, depending on wave conditions and bottom slope.

Q2: How does wave steepness affect the Breaker Depth Index?
A: Steeper waves tend to have higher breaker depth indices, meaning they break in deeper water relative to their height.

Q3: What is the difference between setup and set down?
A: Setup is the wave-induced increase in mean water level, while set down is the wave-induced decrease of mean water level before waves break.

Q4: Can this formula be used for all types of waves?
A: This formula is primarily applicable for regular waves breaking on uniform slopes. Irregular waves or complex bathymetry may require more sophisticated models.

Q5: How accurate is the Breaker Depth Index prediction?
A: The accuracy depends on the quality of input data and how well the actual conditions match the assumptions of the formula. Field measurements provide the most reliable results.