1.4. Conservation of Wave Power

Wave energy flux is the rate at which energy is transmitted in the direction of wave propagation across a vertical plane perpendicular to the direction of wave advance. The average energy flux per unit wave crest transmitted across the plane is called wave power. It is given as e into CG, where CG is group velocity and e is the energy.

Wave power refers to the amount of energy generated by waves as they move through the water. To understand this, first, we need to know about wave energy flux. Energy flux is how quickly energy flows through a specific area, in this case, a vertical plane that cuts through the wave front. Wave power is calculated by multiplying the energy per wave (denoted as 'e') by the group velocity (CG), which tells us how fast the wave energy is traveling.

Imagine standing at the beach watching waves crash on the shore. Each wave carries energy, just like cars carry people as they travel down a highway. If we think of waves as cars, wave power is similar to the number of cars passing a point multiplied by how fast they're going. The faster they go (group velocity) and the more cars there are (energy per wave) means more wave power reaching the shore.

The wave power is conserved if the wave moves from one depth to another. This means the average energy flux per unit wave crest remains constant as the wave travels from deep water to shallow water.

Conservation of wave power tells us that as a wave travels from deep to shallow water, the energy it carries does not disappear; instead, it remains the same. This is important because it allows us to use one known condition (like the wave power in deep water) to understand conditions at any other depth. The average energy flux per wave crest is consistent, which means as waves approach the shore, they maintain their energy even as conditions change.

Think of a water slide at a water park. When a person (representing wave energy) starts at the top (deep water), they have a lot of potential energy. As they slide down (moving to shallow water), the same person has the same energy, but how that energy translates into speed and impact can change. Just like how the wave energy maintains its power from one depth to another, the slider uses that potential energy to maintain speed.

The relationship between wave height in deep water and wave height in shallower waters can be expressed using the shoaling coefficient. This shows how wave height changes as waves propagate from deep to shallow water.

When waves enter shallower waters, their height increases due to the conservation of energy. The shoaling coefficient (denoted as Ks) helps calculate the new wave height at any depth, based on the original height at deeper depths. This idea is crucial for predicting wave behavior in coastal engineering and understanding the potential impact on shorelines.

Imagine a straight river flowing into a narrow canyon. As the water approaches the canyon, it has to move faster and might splash higher because the space is smaller. Similarly, as ocean waves approach the shore (and shallower waters), they climb higher due to the conservation of wave power, similar to how water splashes higher in a constricted space.

As waves move, particles in the water exhibit elliptical or circular motion, advancing a short distance in the direction of wave propagation. This creates what's known as mass transport, where the motion of the wave transports mass in the same direction as the wave progresses.

When waves roll through the ocean, the water particles don't just move up and down—they also move forward in the direction the wave is traveling. This forward movement of particles is called mass transport and occurs during the wave's cycle. It signifies that as waves move, there's a gradual shift of water in the same direction, contributing to currents and energy distribution in the sea.

Consider a group of kids at a pool, jumping up and down on inflatable mats. While they bounce, they also drift toward the edge of the pool due to waves they create. Just like the kids, the water particles move up and down while also moving along with the wave's direction, resulting in a flow of water toward the shore.

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