Wave Height For Major Horizontal Semi-Axis Given Wavelength Calculator

Wave Height Formula:

\[ H = A \times 2 \times \frac{\sinh(2\pi d/\lambda)}{\cosh(2\pi (DZ + d)/\lambda)} \]

Horizontal Semi-axis of Water Particle (A):

Depth of Water Wave (d):

Wavelength (λ):

Distance above Bottom (DZ):

Wave Height (H):

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1. What is the Wave Height Formula?

The Wave Height formula calculates the vertical distance between the trough and crest of a wave based on horizontal semi-axis of water particle, water depth, wavelength, and distance above bottom. This formula is essential for understanding wave behavior in coastal engineering and oceanography.

2. How Does the Calculator Work?

The calculator uses the Wave Height formula:

\[ H = A \times 2 \times \frac{\sinh(2\pi d/\lambda)}{\cosh(2\pi (DZ + d)/\lambda)} \]

Where:

\( H \) — Wave Height (m)
\( A \) — Horizontal Semi-axis of Water Particle (m)
\( d \) — Depth of Water Wave (m)
\( \lambda \) — Wavelength (m)
\( DZ \) — Distance above Bottom (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula uses hyperbolic sine and cosine functions to account for the wave's behavior at different water depths and positions above the seabed.

3. Importance of Wave Height Calculation

Details: Accurate wave height estimation is crucial for coastal engineering, navigation safety, offshore operations, and understanding coastal erosion patterns.

4. Using the Calculator

Tips: Enter all values in meters. Ensure all inputs are positive values (wavelength > 0, depth > 0, horizontal semi-axis > 0, distance above bottom ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of hyperbolic functions in this formula?
A: Hyperbolic functions (sinh and cosh) accurately describe the exponential decay of wave motion with depth, which is characteristic of water waves.

Q2: How does water depth affect wave height?
A: As water depth decreases relative to wavelength (shoaling), waves typically increase in height until they break.

Q3: What is the typical range of wave heights?
A: Wave heights can range from a few centimeters (ripples) to over 30 meters in extreme storm conditions.

Q4: Are there limitations to this formula?
A: This formula assumes linear wave theory and may be less accurate for very steep waves or in shallow water where non-linear effects become significant.

Q5: How is this formula used in practical applications?
A: It's used in coastal engineering for breakwater design, in offshore operations for platform safety, and in navigation for route planning.