Beach Slope Modified For Wave Setup Calculator

Modified Beach Slope Formula:

\[ \beta^* = \arctan\left(\frac{\tan(\beta)}{1 + \frac{3\gamma_b^2}{8}}\right) \]

Modified Beach Slope (β*):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Modified Beach Slope Formula?

The Modified Beach Slope formula calculates the adjusted beach slope for wave setup, which depends on the original beach slope and the breaker depth index. This modification accounts for the effects of wave breaking on beach morphology.

2. How Does the Calculator Work?

The calculator uses the Modified Beach Slope formula:

\[ \beta^* = \arctan\left(\frac{\tan(\beta)}{1 + \frac{3\gamma_b^2}{8}}\right) \]

Where:

\( \beta^* \) — Modified beach slope (radians)
\( \beta \) — Original beach slope (radians)
\( \gamma_b \) — Breaker depth index (-)

Explanation: The formula adjusts the beach slope based on the breaker depth index to account for wave setup effects on beach morphology.

3. Importance of Modified Beach Slope Calculation

Details: Accurate modified beach slope calculation is crucial for coastal engineering, sediment transport studies, and predicting beach erosion and accretion patterns under different wave conditions.

4. Using the Calculator

Tips: Enter beach slope in radians and breaker depth index as a dimensionless value. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the breaker depth index?
A: Breaker depth index is the ratio of wave height at breaking to the water depth at the breakpoint, typically ranging from 0.3 to 1.2.

Q2: Why modify the beach slope for wave setup?
A: Wave setup affects the effective beach slope, which influences sediment transport patterns and beach morphology changes.

Q3: What are typical values for beach slope?
A: Beach slopes typically range from 0.02 to 0.2 radians (approximately 1-12 degrees), depending on sediment characteristics and wave conditions.

Q4: How does breaker depth index affect the modified slope?
A: Higher breaker depth indices result in greater modification of the beach slope, reducing the effective slope value.

Q5: What are the limitations of this formula?
A: The formula assumes certain wave conditions and may be less accurate for extreme beach slopes or unusual wave climates.