Maximum Wave Height Using Miche Criterion Calculator

Miche Criterion Formula:

\[ H_{max} = 0.14 \times \lambda \times \tanh(d \times k) \]

Maximum Wave Height (H_max):

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1. What is the Miche Criterion?

The Miche Criterion is an empirical formula used to estimate the maximum wave height in coastal waters. It relates wave height to wavelength, water depth, and wave number, providing a practical approach for coastal engineering applications.

2. How Does the Calculator Work?

The calculator uses the Miche Criterion formula:

\[ H_{max} = 0.14 \times \lambda \times \tanh(d \times k) \]

Where:

\( H_{max} \) — Maximum Wave Height (m)
\( \lambda \) — Wavelength of Coast (m)
\( d \) — Water Depth (m)
\( k \) — Wave Number for Waves in Coast (rad/m)
\( \tanh \) — Hyperbolic tangent function

Explanation: The formula accounts for the relationship between wave characteristics and water depth, with the hyperbolic tangent function modeling how waves behave in different depth conditions.

3. Importance of Maximum Wave Height Calculation

Details: Accurate maximum wave height estimation is crucial for coastal structure design, maritime operations, flood risk assessment, and understanding coastal processes and erosion patterns.

4. Using the Calculator

Tips: Enter wavelength in meters, water depth in meters, and wave number in radians per meter. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of maximum wave heights in coastal areas?
A: Maximum wave heights can vary significantly, typically ranging from less than 1 meter in sheltered areas to over 15 meters during extreme storm conditions in exposed coastal regions.

Q2: How does water depth affect maximum wave height?
A: Water depth significantly influences wave behavior. In shallow water, waves tend to steepen and break, limiting their maximum height, while in deep water, waves can achieve greater heights.

Q3: What are the limitations of the Miche Criterion?
A: The Miche Criterion provides an empirical estimate and may not account for all factors affecting wave height, such as wind duration, fetch length, bottom topography variations, and nonlinear wave interactions.

Q4: How is wave number related to wavelength?
A: Wave number (k) is inversely related to wavelength (λ) through the formula \( k = \frac{2\pi}{\lambda} \), where wave number represents the spatial frequency of the wave.

Q5: When should the Miche Criterion be used versus other wave height formulas?
A: The Miche Criterion is particularly useful for estimating maximum wave heights in coastal and shallow water environments. Other formulas may be more appropriate for deep water conditions or specific wave generation mechanisms.