Scaling Parameter Calculator

Dimensionless Scaling Parameter Formula:

\[ \alpha = 0.076 \times \left( \frac{[g] \times F_l}{V_{10}^2} \right)^{-0.22} \]

Dimensionless Scaling Parameter (α):

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1. What is the Dimensionless Scaling Parameter?

The Dimensionless Scaling Parameter is a value used in mathematical or scientific models to scale or normalize variables without units. It is particularly used in the JONSWAP spectrum for fetch-limited seas to characterize wave development under specific wind conditions.

2. How Does the Calculator Work?

The calculator uses the scaling parameter formula:

\[ \alpha = 0.076 \times \left( \frac{[g] \times F_l}{V_{10}^2} \right)^{-0.22} \]

Where:

\( \alpha \) — Dimensionless Scaling Parameter
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( F_l \) — Fetch Length (meters)
\( V_{10} \) — Wind Speed at 10m height (m/s)

Explanation: This formula calculates the scaling parameter that describes how wave energy develops under given wind conditions over a specific fetch length.

3. Importance of Scaling Parameter Calculation

Details: The scaling parameter is crucial for predicting wave characteristics in fetch-limited conditions. It helps in oceanographic studies, coastal engineering, and maritime operations by providing insights into wave energy distribution and development.

4. Using the Calculator

Tips: Enter fetch length in meters and wind speed at 10m height in meters per second. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is fetch length in oceanography?
A: Fetch length is the unobstructed distance that wind can travel over water in a constant direction, which directly affects wave development and size.

Q2: Why is wind speed measured at 10m height?
A: Wind speed at 10m height is a standard reference height in meteorology and oceanography to minimize surface effects and provide consistent measurements.

Q3: What is the JONSWAP spectrum?
A: The JONSWAP (Joint North Sea Wave Observation Project) spectrum is a parametric model that describes the distribution of wave energy over frequency for fetch-limited sea states.

Q4: What are typical values for the scaling parameter?
A: The scaling parameter typically ranges from 0.008 to 0.015 for fully developed seas, but can vary significantly depending on fetch conditions and wind speed.

Q5: How does this parameter affect wave prediction?
A: The scaling parameter directly influences the peak energy and overall shape of the wave spectrum, affecting predictions of significant wave height, peak period, and wave energy distribution.