Maximum Wave Height Given Energy Dissipation Rate Calculator

Maximum Wave Height Formula:

\[ H_{max} = \sqrt{\frac{\delta}{0.25 \times \rho_{water} \times [g] \times Q_B \times f_m}} \]

Energy Dissipation Rate per unit Surface Area:

J/m²/s

Water Density:

kg/m³

Percentage of Waves Breaking:

Mean Wave Frequency:

Maximum Wave Height:

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1. What is the Maximum Wave Height Formula?

The Maximum Wave Height formula calculates the most probable maximum wave height based on energy dissipation rate, water density, percentage of waves breaking, and mean wave frequency. This is important for coastal engineering and oceanography applications.

2. How Does the Calculator Work?

The calculator uses the Maximum Wave Height formula:

\[ H_{max} = \sqrt{\frac{\delta}{0.25 \times \rho_{water} \times [g] \times Q_B \times f_m}} \]

Where:

\( H_{max} \) — Maximum Wave Height (m)
\( \delta \) — Energy Dissipation Rate per unit Surface Area (J/m²/s)
\( \rho_{water} \) — Water Density (kg/m³)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( Q_B \) — Percentage of Waves Breaking (%)
\( f_m \) — Mean Wave Frequency (Hz)

Explanation: The formula calculates the maximum wave height by considering the energy dissipation characteristics and wave properties.

3. Importance of Maximum Wave Height Calculation

Details: Accurate maximum wave height estimation is crucial for coastal structure design, ship navigation safety, offshore operations, and understanding coastal erosion processes.

4. Using the Calculator

Tips: Enter energy dissipation rate in J/m²/s, water density in kg/m³, percentage of waves breaking as a percentage value, and mean wave frequency in Hz. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is energy dissipation rate per unit surface area?
A: It represents the amount of wave energy lost due to viscous forces and wave breaking per unit area of the water surface.

Q2: Why is gravitational acceleration included in the formula?
A: Gravitational acceleration affects wave dynamics and energy dissipation processes, making it an essential factor in wave height calculations.

Q3: How is percentage of waves breaking determined?
A: This is typically measured through field observations or calculated based on wave steepness and water depth conditions.

Q4: What are typical values for mean wave frequency?
A: Ocean waves typically have frequencies between 0.05-0.3 Hz, while wind waves can have higher frequencies up to 1 Hz.

Q5: Are there limitations to this formula?
A: The formula assumes steady-state conditions and may be less accurate for rapidly changing wave conditions or extreme weather events.