Wave Height Given Mean Water Surface Elevation Set Down For Regular Waves Calculator

Formula Used:

\[ H = \sqrt{\eta'_o \times 8 \times \sinh\left(\frac{4\pi d}{\lambda}\right) \div \left(\frac{2\pi}{\lambda}\right)} \]

Wave Height (H):

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1. What is the Wave Height Formula?

The wave height formula calculates the height of surface waves based on mean water surface elevation, water depth, and wavelength. It provides an accurate assessment of wave characteristics in coastal environments.

2. How Does the Calculator Work?

The calculator uses the wave height formula:

\[ H = \sqrt{\eta'_o \times 8 \times \sinh\left(\frac{4\pi d}{\lambda}\right) \div \left(\frac{2\pi}{\lambda}\right)} \]

Where:

\( H \) — Wave Height (m)
\( \eta'_o \) — Mean Water Surface Elevation of Coast (m)
\( d \) — Water Depth (m)
\( \lambda \) — Wavelength of Coast (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula accounts for the relationship between water surface elevation, depth, wavelength, and resulting wave height using hyperbolic sine function.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, beach erosion studies, and marine construction projects.

4. Using the Calculator

Tips: Enter mean water surface elevation in meters, water depth in meters, and wavelength in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is mean water surface elevation?
A: Mean water surface elevation refers to the average height of the water surface in relation to a reference level, typically mean sea level.

Q2: How does water depth affect wave height?
A: Water depth significantly influences wave characteristics. As waves approach shallower water, they typically increase in height due to shoaling effects.

Q3: What is wavelength in coastal context?
A: Wavelength refers to the distance between two successive wave crests or troughs as waves travel through water near the shore.

Q4: Are there limitations to this formula?
A: This formula works best for regular waves in specific conditions. It may be less accurate for irregular waves or extreme environmental conditions.

Q5: What applications use wave height calculations?
A: Coastal engineering, marine navigation, offshore construction, surfing forecasts, and climate change impact studies all utilize wave height calculations.