1. What is the Wave Height Formula?

The Wave Height formula calculates the vertical distance between the trough and crest of a wave based on vertical semi-axis, water depth, wavelength, and distance above bottom. This formula is essential in oceanography and coastal engineering for understanding wave behavior.

2. How Does the Calculator Work?

The calculator uses the Wave Height formula:

Where:

• \( H \) — Wave Height (m)
• \( B \) — Vertical Semi-Axis (m)
• \( d \) — Depth of Water Wave (m)
• \( \lambda \) — Wavelength (m)
• \( DZ \) — Distance above Bottom (m)
• \( \pi \) — Archimedes' constant (approximately 3.14159)
• \( \sinh \) — Hyperbolic sine function

Explanation: The formula accounts for the hyperbolic relationship between wave parameters and water depth, providing accurate wave height estimation.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, offshore operations, and understanding coastal erosion patterns.

4. Using the Calculator

Tips: Enter all values in meters. Vertical Semi-Axis, Depth of Water Wave, and Wavelength must be positive values. Distance above Bottom must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is Vertical Semi-Axis?
A: Vertical Semi-Axis represents half of the vertical distance from the wave crest to trough in the elliptical motion of water particles.

Q2: Why use hyperbolic sine functions?
A: Hyperbolic sine functions accurately model the decay of wave motion with depth in fluid dynamics.

Q3: What are typical wavelength values?
A: Wavelengths can vary from a few meters for wind waves to hundreds of meters for swell waves in deep water.

Q4: How does water depth affect wave height?
A: As waves approach shallower water, their height typically increases due to shoaling effects before breaking.

Q5: When is this formula most accurate?
A: This formula provides good accuracy for linear wave theory applications in intermediate water depths.