Wave Height When Free Surface Elevation Of Solitary Waves Calculator

Formula Used:

\[ Hw' = \eta \times \frac{\sqrt{[g] \times dc}}{u \times dc} \]

Cnoidal Wave Height (Hw'):

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1. What is the Wave Height When Free Surface Elevation Of Solitary Waves Formula?

The Wave Height When Free Surface Elevation Of Solitary Waves formula calculates the cnoidal wave height from free surface elevation, water depth, and particle velocity. It provides an accurate assessment of wave characteristics in cnoidal wave theory.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Hw' = \eta \times \frac{\sqrt{[g] \times dc}}{u \times dc} \]

Where:

\( Hw' \) — Cnoidal Wave Height (m)
\( \eta \) — Free Surface Elevation (m)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( dc \) — Water Depth for Cnoidal Wave (m)
\( u \) — Particle Velocity (m/s)

Explanation: The formula relates wave height to free surface elevation, water depth, and particle velocity using gravitational acceleration as a constant factor.

3. Importance of Cnoidal Wave Height Calculation

Details: Accurate wave height calculation is crucial for coastal engineering, wave prediction, and understanding wave behavior in various water depth conditions.

4. Using the Calculator

Tips: Enter free surface elevation in meters, water depth in meters, and particle velocity in m/s. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are cnoidal waves?
A: Cnoidal waves are exact periodic wave solutions of the Korteweg-de Vries equation, characterized by their cnoidal (elliptic function) shape.

Q2: When is this formula applicable?
A: This formula is specifically designed for calculating wave height in cnoidal wave theory, particularly for solitary waves.

Q3: What is the typical range of cnoidal wave heights?
A: Cnoidal wave heights vary depending on water depth and wave conditions, typically ranging from centimeters to several meters.

Q4: Are there limitations to this formula?
A: This formula assumes ideal conditions and may have limitations in complex real-world scenarios with varying bottom topography.

Q5: How does water depth affect cnoidal wave height?
A: Water depth significantly influences wave characteristics, with shallower depths generally producing higher waves relative to depth.