Calculate Breaking Wave Height
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Waves are a fundamental aspect of oceanography and coastal engineering. Understanding wave breaking is crucial for predicting wave behavior, designing coastal structures, and assessing wave energy potential. This guide explains how to calculate breaking wave height, the factors that influence it, and how to interpret the results.
Introduction
Waves are formed by the transfer of energy from the wind to the water surface. As wind blows over the ocean, it creates ripples that grow into waves. The height of a wave is determined by the wind speed, duration, and fetch (the distance over which the wind blows).
When waves reach shallow water or encounter obstacles, they can break. Wave breaking is a complex process that involves the wave's energy being dissipated as it collapses. The breaking wave height is a critical parameter in coastal engineering and oceanography.
Wave Breaking Criteria
Waves break when the wave height becomes too large relative to the water depth. The most common breaking criteria are:
- Stokes' breaking criterion: A wave breaks when the wave height (H) exceeds 0.78 times the water depth (d).
- Battjes' breaking criterion: A wave breaks when the wave height exceeds 0.5 times the water depth.
- Shoaling breaking criterion: A wave breaks when the wave height exceeds 0.14 times the water depth.
These criteria are empirical and have been derived from observations of breaking waves in the field.
Breaking Wave Height Formula
The breaking wave height can be calculated using the following formula:
Where:
- H_breaking is the breaking wave height
- k is the breaking coefficient (typically between 0.14 and 0.78)
- d is the water depth
The breaking coefficient (k) depends on the breaking criterion used. For Stokes' criterion, k = 0.78, and for Battjes' criterion, k = 0.5.
Wave Height Comparison
The following table compares the breaking wave height for different water depths using different breaking criteria:
| Water Depth (m) | Stokes' (k=0.78) | Battjes' (k=0.5) | Shoaling (k=0.14) |
|---|---|---|---|
| 5 | 3.9 | 2.5 | 0.7 |
| 10 | 7.8 | 5.0 | 1.4 |
| 20 | 15.6 | 10.0 | 2.8 |
| 50 | 39.0 | 25.0 | 7.0 |
This table shows how the breaking wave height varies with water depth for different breaking criteria. The Stokes' criterion generally predicts the largest breaking wave heights, while the shoaling criterion predicts the smallest.
Frequently Asked Questions
What is the difference between wave height and wave period?
Wave height is the vertical distance between the crest and the trough of a wave, while wave period is the time interval between two consecutive wave crests passing a fixed point.
How does water depth affect wave breaking?
Water depth plays a crucial role in wave breaking. As waves enter shallower water, their height increases relative to the water depth, leading to breaking. The breaking criteria provide empirical relationships between wave height and water depth.
What are the different types of wave breaking?
Wave breaking can be classified into spilling breakers, plunging breakers, and surging breakers. Spilling breakers occur on gentle slopes, while plunging breakers occur on steeper slopes. Surging breakers are a combination of spilling and plunging breakers.