Wave Height Given Radiation Stress Component Calculator

Wave Height Formula:

\[ H = \sqrt{\frac{S_{xy} \times 8}{\rho \times g \times \cos(\alpha) \times \sin(\alpha)}} \]

Wave Height (H):

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1. What is Wave Height?

Wave Height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. It's a fundamental parameter in oceanography and coastal engineering that describes the vertical distance between the wave crest and the adjacent wave trough.

2. How Does the Calculator Work?

The calculator uses the wave height formula:

\[ H = \sqrt{\frac{S_{xy} \times 8}{\rho \times g \times \cos(\alpha) \times \sin(\alpha)}} \]

Where:

\( H \) — Wave Height (m)
\( S_{xy} \) — Radiation Stress Component (N/m)
\( \rho \) — Mass Density (kg/m³)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( \alpha \) — Wave Crest Angle (radians)

Explanation: The formula calculates wave height based on radiation stress component, water density, gravitational acceleration, and wave crest angle using trigonometric functions.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, offshore operations, and understanding coastal processes and sediment transport.

4. Using the Calculator

Tips: Enter radiation stress component in N/m, mass density in kg/m³, and wave crest angle in radians. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is radiation stress component?
A: Radiation Stress Component is the momentum transferred through the water body per unit of time by wave orbital motion.

Q2: Why is wave crest angle important?
A: Wave crest angle determines how wave energy is distributed and affects wave transformation processes near shorelines.

Q3: What are typical wave height values?
A: Wave heights vary from centimeters (ripples) to over 30 meters (extreme storm waves) depending on wind conditions and fetch.

Q4: How does water density affect wave height?
A: Higher density water requires more energy to create the same wave height, making density a crucial factor in the calculation.

Q5: Are there limitations to this equation?
A: This formula works best for linear wave theory conditions and may need adjustments for extreme waves or complex bathymetry.