A solitary wave, also known as a "wave of translation," is a single, crest-shaped wave that moves over the water surface without changing its shape or speed.
Unlike regular waves, which have both crests and troughs and rise and fall - called oscillatory waves - a solitary wave consists only of a crest and does not have a corresponding trough.
It's a smooth hump of water that stays entirely above the calm water level.
As it travels, it pushes water forward as it moves, carrying objects (like a floating leaf) a short distance before stopping them, resulting in a net movement of water.
Again, unlike ordinary ocean waves, which pull objects back and forth.
Formation of Solitary Waves
Solitary waves form when a sudden disturbance adds a mass of water to a still surface.
It can happen when a wave breaks and the water from the crest falls onto the surface ahead, creating a single, hump-like wave that moves forward.
The process is common in shallow waters near shorelines, especially after waves break and transform into waves of translation.
It doesn't exist in deep, open oceans.
Historical Observation
The first recorded observation of a solitary wave was by Scottish engineer John Scott Russell in 1834.
While studying canal boat designs, he noticed a unique wave phenomenon.
As he described, after a boat stopped suddenly in a narrow channel, the water it had set in motion continued forward, forming a large, solitary elevation - a smooth, well-defined heap of water - that maintained its shape and speed over a considerable distance.
Russell followed this wave on horseback for one or two miles before losing sight of it in the channel's windings.
He coined this phenomenon the "wave of translation" because it physically transports water forward.
Characteristics of Solitary Waves
As we've already seen above, solitary waves have unique features that set them apart from regular oscillatory waves.
Here's a short summary of their main characteristics.
1. Single Crest
The entire wave is above the undisturbed water level, consisting solely of a crest without an accompanying trough.
2. Particle Movement
As the wave passes, water particles are carried forward and do not return to their original position.
For example, an object floating on the water would be pushed forward by the wave and then come to rest without moving backward as it would with regular waves.
3. Speed and Size Relationship
The speed of a solitary wave depends on both the water depth and the wave's height.
Specifically, the wave's speed (C) can be calculated using the formula C = √g(d + h), where g is the acceleration due to gravity, d is the water depth, and h is the wave height.
As a result, taller waves in deeper water move faster.
When multiple solitary waves travel together, later ones often speed up and overtake earlier ones.
Why? Each new wave rides on top of the previous one, effectively moving through deeper water.
4. Stability
These waves are stable and can travel long distances without changing shape, unlike regular waves that may flatten out or break.
Where Can We See Them?
Solitary waves are typically found in shallow waters, especially near coastlines, where waves break and transform into waves of translation.
They are not present in the open sea but become significant in shallow areas inside the breakers.
Notably, solitary waves have been observed from space and are frequently seen at the Strait of Gibraltar, the entrance to the Mediterranean Sea.
Scientists can also generate solitary waves in wave tanks, like the 104-meter-long tank at Oregon State University's O. H. Hinsdale Wave Research Laboratory.
They are made by moving plates in these massive enclosed water containers to understand their behavior better and study coastal erosion, seaside engineering, navigation, and predicting the impact of large waves on shorelines.
Words by Luís MP | Founder of SurferToday.com
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