Deepwater Wave Height Given Nonbreaking Upper Limit Of Runup On Uniform Slope Calculator

Formula Used:

\[ \text{Deepwater Wave Height} = \frac{\text{Wave Runup}}{\sqrt{2\pi} \times \left(\frac{\pi}{2} \times \text{Beach Slope}\right)^{1/4}} \]

Deepwater Wave Height (Hd):

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1. What is Deepwater Wave Height?

Deepwater Wave Height refers to the measurement of the vertical distance between the trough and the crest of a wave in deep water. It is a crucial parameter in coastal engineering and oceanography for understanding wave behavior and its impact on shorelines.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the deepwater wave height based on wave runup and beach slope, providing an estimate of wave characteristics in deep water conditions.

3. Importance of Deepwater Wave Height Calculation

Details: Accurate deepwater wave height estimation is essential for coastal structure design, shoreline protection, and understanding wave energy transformation from deep to shallow water.

4. Using the Calculator

Tips: Enter wave runup in meters and beach slope as a dimensionless value. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is wave runup?
A: Wave runup is the maximum onshore elevation reached by waves, relative to the shoreline position in the absence of waves.

Q2: How is beach slope measured?
A: Beach slope is typically measured as the ratio of vertical rise to horizontal distance, often expressed as a dimensionless value or in degrees.

Q3: What are typical values for beach slope?
A: Beach slopes typically range from 0.01 (gentle) to 0.1 (steep), depending on sediment characteristics and wave conditions.

Q4: When is this formula applicable?
A: This formula applies to nonbreaking wave conditions on uniform slopes and provides the upper limit of runup estimation.

Q5: Are there limitations to this equation?
A: This equation assumes uniform slope conditions and nonbreaking waves. It may not be accurate for complex bathymetry or breaking wave conditions.