Wave Height Of Unbroken Wave In Water Of Finite Depth Calculator

Wave Height Formula:

\[ H_w = D_w \times \frac{0.141063 \times \frac{L}{D_w} + 0.0095721 \times (\frac{L}{D_w})^2 + 0.0077829 \times (\frac{L}{D_w})^3}{1 + 0.078834 \times \frac{L}{D_w} + 0.0317567 \times (\frac{L}{D_w})^2 + 0.0093407 \times (\frac{L}{D_w})^3} \times a_s \]

Height of the Wave (H_w):

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1. What is the Wave Height Formula?

The wave height formula calculates the height of unbroken waves in water of finite depth. It accounts for the relationship between water depth, wave length, and solitary wave amplitude to determine the vertical distance between wave crest and trough.

2. How Does the Calculator Work?

The calculator uses the wave height formula:

Where:

\( H_w \) — Height of the Wave (m)
\( D_w \) — Water Depth from Bed (m)
\( L \) — Length of Water Wave (m)
\( a_s \) — Solitary Wave Amplitude (m)

Explanation: The formula calculates wave height based on the ratio of wave length to water depth, with polynomial coefficients that model the wave behavior in finite depth conditions.

3. Importance of Wave Height Calculation

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

4. Using the Calculator

Tips: Enter water depth, wave length, and solitary wave amplitude in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between wave height and wave amplitude?
A: Wave height is the vertical distance between crest and trough, while wave amplitude is half the wave height (distance from still water level to crest).

Q2: How does water depth affect wave height?
A: In shallow water, waves slow down and their height increases as wave energy is compressed into a smaller water column.

Q3: What are typical wave height ranges?
A: Wave heights can range from a few centimeters (ripples) to over 30 meters (extreme storm waves) in open ocean conditions.

Q4: When is this formula most accurate?
A: This formula works best for unbroken waves in intermediate water depths where both depth and wavelength significantly influence wave behavior.

Q5: How does this differ from deep water wave formulas?
A: Deep water formulas assume infinite depth and don't account for bottom effects, while this finite depth formula includes the influence of the seabed on wave characteristics.