Water Depth Given Maximum Wave Height By Miche Criterion Calculator

Miche Criterion Equation:

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

Maximum Wave Height (Hmax):

Wavelength of Coast (λ):

Wave Number for Waves in Coast (k):

rad/m

Water Depth (d):

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1. What is the Miche Criterion?

The Miche Criterion is an equation used in coastal engineering to estimate water depth based on wave characteristics. It relates maximum wave height, wavelength, and wave number to determine the water depth at a particular location.

2. How Does the Calculator Work?

The calculator uses the Miche Criterion equation:

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

Where:

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

Explanation: The equation uses the inverse hyperbolic tangent function to relate wave characteristics to water depth, providing an estimate based on the maximum wave height criterion.

3. Importance of Water Depth Calculation

Details: Accurate water depth estimation is crucial for coastal engineering, navigation safety, sediment transport studies, and understanding wave behavior in shallow water environments.

4. Using the Calculator

Tips: Enter maximum wave height in meters, wavelength in meters, and wave number in radians per meter. All values must be positive and Hmax/(0.14*λ) must be between -1 and 1 for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of the Miche Criterion?
A: The Miche Criterion helps determine the maximum wave height that can be supported in water of a given depth, which is important for understanding wave breaking and coastal processes.

Q2: What are typical values for wave number in coastal areas?
A: Wave number typically ranges from 0.01 to 0.2 rad/m for ocean waves, with higher values indicating shorter wavelengths.

Q3: When is this calculation most accurate?
A: The Miche Criterion is most accurate for intermediate water depths and regular wave conditions. It may be less accurate for very shallow or very deep water extremes.

Q4: Are there limitations to this equation?
A: The equation assumes ideal wave conditions and may not account for complex bathymetry, currents, or irregular wave spectra found in real coastal environments.

Q5: How does water depth affect wave characteristics?
A: Water depth significantly affects wave speed, wavelength, and wave height through shoaling processes. As waves approach shallow water, they slow down, wavelength decreases, and wave height increases until breaking occurs.