Free Surface Elevation of Solitary Waves Calculator

Free Surface Elevation Formula:

\[ \eta = H_w \times \left( \frac{u}{\sqrt{[g] \times d_c} \times \left( \frac{H_w}{d_c} \right)} \right) \]

Free Surface Elevation (η):

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1. What is Free Surface Elevation?

Free Surface Elevation refers to the instantaneous vertical displacement of the water surface caused by various factors such as waves, tides, currents, and atmospheric conditions. It is a crucial parameter in coastal engineering and oceanography.

2. How Does the Calculator Work?

The calculator uses the Free Surface Elevation formula:

\[ \eta = H_w \times \left( \frac{u}{\sqrt{[g] \times d_c} \times \left( \frac{H_w}{d_c} \right)} \right) \]

Where:

\( \eta \) — Free Surface Elevation (m)
\( H_w \) — Height of the Wave (m)
\( u \) — Particle Velocity (m/s)
\( d_c \) — Water Depth for Cnoidal Wave (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)

Explanation: This formula calculates the free surface elevation of solitary waves based on wave height, particle velocity, and water depth.

3. Importance of Free Surface Elevation Calculation

Details: Accurate calculation of free surface elevation is essential for coastal structure design, flood prediction, navigation safety, and understanding wave behavior in various water depths.

4. Using the Calculator

Tips: Enter wave height in meters, particle velocity in m/s, and water depth in meters. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What are solitary waves?
A: Solitary waves are single, hump-shaped waves that maintain their shape and speed while propagating in water of constant depth.

Q2: How does water depth affect free surface elevation?
A: Water depth significantly influences wave behavior. In shallower water, waves tend to become steeper and free surface elevation increases.

Q3: What is particle velocity in wave context?
A: Particle velocity refers to the velocity at which water particles move as a result of wave passage, typically following orbital paths.

Q4: Are there limitations to this equation?
A: This equation is specifically designed for cnoidal/solitary waves and may not be accurate for other wave types or in extreme conditions.

Q5: What practical applications use free surface elevation calculations?
A: Coastal engineering, tsunami modeling, offshore structure design, and environmental impact assessments all rely on accurate free surface elevation calculations.