JONSWAP Spectrum For Fetch-limited Seas Calculator

JONSWAP Spectrum Equation:

\[ E_f = \frac{\alpha \cdot g^2}{(2\pi)^4 \cdot f^5} \cdot \left( \exp\left(-1.25 \cdot \left(\frac{f}{f_p}\right)^{-4}\right) \cdot \gamma \right)^{\exp\left(-\frac{\left(\frac{f}{f_p}-1\right)^2}{2\sigma^2}\right)} \]

Dimensionless Scaling Parameter (α):

Wave Frequency (f):

Frequency at Spectral Peak (fₚ):

Peak Enhancement Factor (γ):

Standard Deviation (σ):

Frequency Energy Spectrum (Ef):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the JONSWAP Spectrum?

The JONSWAP (Joint North Sea Wave Observation Project) spectrum is an empirical wave spectrum model developed for fetch-limited seas. It describes the distribution of wave energy across different frequencies in ocean waves, particularly in developing sea states.

2. How Does the Calculator Work?

The calculator uses the JONSWAP spectrum equation:

Where:

\( \alpha \) — Dimensionless scaling parameter (typically 0.0081)
\( g \) — Gravitational acceleration (9.80665 m/s²)
\( f \) — Wave frequency (Hz)
\( f_p \) — Frequency at spectral peak (Hz)
\( \gamma \) — Peak enhancement factor (typically 3.3)
\( \sigma \) — Standard deviation (0.07 for f ≤ fₚ, 0.09 for f > fₚ)

Explanation: The equation models the energy distribution of ocean waves, accounting for the peak enhancement and spectral shape characteristics of fetch-limited seas.

3. Importance of Wave Spectrum Analysis

Details: Wave spectrum analysis is crucial for offshore engineering, coastal management, ship design, and understanding ocean dynamics. The JONSWAP spectrum provides accurate predictions for developing sea states with limited fetch.

4. Using the Calculator

Tips: Enter all parameters as positive values. Typical values: α = 0.0081, γ = 3.3, σ = 0.07-0.09. Ensure frequency values are in Hz and all inputs are valid.

5. Frequently Asked Questions (FAQ)

Q1: What is fetch-limited sea?
A: Fetch-limited sea refers to ocean conditions where wave growth is limited by the distance over which wind can generate waves (fetch), rather than by wind duration.

Q2: How does JONSWAP differ from Pierson-Moskowitz spectrum?
A: JONSWAP includes a peak enhancement factor (γ) that makes the spectrum more peaked than the Pierson-Moskowitz spectrum, better representing developing sea states.

Q3: What are typical values for the peak enhancement factor?
A: The peak enhancement factor γ typically ranges from 1 to 7, with an average value of 3.3 for the North Sea data.

Q4: When should the JONSWAP spectrum be used?
A: JONSWAP is particularly suitable for fetch-limited seas and developing wave conditions, commonly used in coastal engineering and offshore design applications.

Q5: How does the standard deviation parameter vary?
A: The standard deviation σ typically takes different values on either side of the peak frequency: σ = 0.07 for f ≤ fₚ and σ = 0.09 for f > fₚ.