Nonbreaking Upper Limit Of Runup On Uniform Slope Calculator

Wave Runup Formula:

\[ R = H_d \times (2\pi)^{0.5} \times \left(\frac{\pi}{2\beta}\right)^{1/4} \]

Wave Runup (R):

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1. What is Wave Runup?

Wave Runup is the maximum onshore elevation reached by waves, relative to the shoreline position in the absence of waves. It represents the upper limit of wave action on a uniform slope without wave breaking.

2. How Does the Calculator Work?

The calculator uses the Wave Runup formula:

\[ R = H_d \times (2\pi)^{0.5} \times \left(\frac{\pi}{2\beta}\right)^{1/4} \]

Where:

\( R \) — Wave Runup (m)
\( H_d \) — Deepwater Wave Height (m)
\( \beta \) — Beach Slope (radians)
\( \pi \) — Archimedes' constant (approximately 3.1416)

Explanation: This formula calculates the nonbreaking upper limit of runup on a uniform slope, considering deepwater wave characteristics and beach geometry.

3. Importance of Wave Runup Calculation

Details: Accurate wave runup estimation is crucial for coastal engineering, shoreline protection design, flood risk assessment, and coastal zone management. It helps determine safe building setbacks and design effective coastal defenses.

4. Using the Calculator

Tips: Enter deepwater wave height in meters and beach slope in radians. Both values must be positive numbers. The beach slope should be measured as the angle from horizontal in radians.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a typical beach slope value?
A: Beach slopes typically range from 0.02 to 0.2 radians (approximately 1-12 degrees), depending on beach composition and wave conditions.

Q2: How does wave height affect runup?
A: Runup increases proportionally with deepwater wave height. Larger waves generate higher runup levels on the shoreline.

Q3: Why is this considered the "nonbreaking" limit?
A: This formula applies to conditions where waves do not break before reaching the shore, representing the theoretical maximum runup for unbroken waves.

Q4: What are the limitations of this formula?
A: This formula assumes uniform slope, nonbreaking waves, and doesn't account for factors like wave period, bottom friction, or complex bathymetry.

Q5: How is beach slope typically measured?
A: Beach slope can be measured through field surveys, topographic maps, or remote sensing techniques, and should be converted to radians for calculation.