Wave Number Given Maximum Wave Height By Miche Criterion Calculator

Wave Number Formula:

\[ k = \frac{\tanh^{-1}\left(\frac{H_{max}}{0.14 \cdot \lambda}\right)}{d} \]

Wave Number for Waves in Coast (k):

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1. What is the Wave Number Formula?

The wave number formula based on the Miche Criterion calculates the spatial frequency of waves in coastal areas using maximum wave height, wavelength, and water depth. It provides a mathematical relationship between these fundamental wave parameters.

2. How Does the Calculator Work?

The calculator uses the wave number formula:

\[ k = \frac{\tanh^{-1}\left(\frac{H_{max}}{0.14 \cdot \lambda}\right)}{d} \]

Where:

\( k \) — Wave number for waves in coast (rad/m)
\( H_{max} \) — Maximum wave height (m)
\( \lambda \) — Wavelength of coast (m)
\( d \) — Water depth (m)
\( \tanh^{-1} \) — Inverse hyperbolic tangent function

Explanation: The formula calculates wave number by considering the ratio of maximum wave height to wavelength and normalizing it with water depth using the inverse hyperbolic tangent function.

3. Importance of Wave Number Calculation

Details: Wave number is crucial for understanding wave behavior in coastal environments, predicting wave propagation, designing coastal structures, and analyzing sediment transport patterns.

4. Using the Calculator

Tips: Enter maximum wave height in meters, wavelength in meters, and water depth in meters. All values must be positive. The ratio Hmax/(0.14*λ) must be between -1 and 1 for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is wave number in coastal engineering?
A: Wave number represents the spatial frequency of waves, measured in radians per meter, indicating how many wave cycles occur per unit distance.

Q2: What is the Miche Criterion?
A: The Miche Criterion is an empirical relationship that describes the maximum wave height limitation based on water depth and wavelength in coastal areas.

Q3: Why use inverse hyperbolic tangent in this formula?
A: The inverse hyperbolic tangent function helps transform the wave height-to-wavelength ratio into a form that properly scales with water depth for wave number calculation.

Q4: What are typical wave number values in coastal areas?
A: Wave numbers typically range from 0.01 to 0.5 rad/m in coastal environments, depending on wave conditions and water depth.

Q5: When is this formula most applicable?
A: This formula is particularly useful for waves in intermediate to shallow water depths where the Miche Criterion applies for wave height limitation.