1.1. Wave Energy Flux

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.

Wave energy flux represents how much energy the waves carry as they move forward. This energy is measured per unit of wave crest, across a surface area that is perpendicular to the direction the wave is traveling. Essentially, it's a measure of the energy density of waves as they pass through a given area, providing insight into their potential power.

Think of wave energy flux like a river flowing with water. The energy in the waves is similar to the volume of water moving past a certain point in the river; the more water, the more energy. If you were to place a paddle in the river at a specific point, the force of the water hitting it would be similar to measuring the wave energy flux.

The average energy flux per unit wave crest transmitted across the plane perpendicular to the wave advance is wave power, given as e into CG.

Wave power is calculated using the formula where 'e' is the energy of the wave, and 'CG' represents the group velocity. The product of these two gives us the total power associated with the wave. This is important because understanding how to quantify wave power is necessary for harnessing wave energy effectively.

Imagine an assembly line where workers (the waves) are moving items (the energy). The efficiency of the assembly line can be considered as wave power, which depends on how many workers are moving items (energy 'e') and how quickly they are moving (group velocity 'CG'). More workers and higher speeds result in greater productivity or power.

Wave power is going to be conserved if the wave moves from one depth to another.

As waves travel from deep to shallow waters, the total energy (or power) they carry remains constant assuming no energy is lost. This conservation principle helps in understanding how waves behave as they interact with different seabed structures or topographies.

Consider a balloon filled with air: as you push it into shallow water, the total volume of air remains constant (just like the wave power), but its shape may change based on the surrounding pressure of the water at different depths. This analogy highlights the conservation principle as the balloon's air moves in response to the environment.

The relationship between wave height at different depths can be described using the shoaling coefficient.

The shoaling coefficient helps quantify how wave height changes as waves approach shallower depths. It relates the wave height in deep water to that in shallower regions, indicating that waves tend to grow taller as they move into shallower water due to conservation of energy.

Imagine a person running on a track that gradually slopes upwards. As they run up the slope, they need to exert more energy and may run faster, making them appear taller as they move. Similarly, waves increase in height as they move into shallow water where the energy from the waves is conserved and concentrated.

The mass transport associated with wave motion suggests that particles complete nearly circular or elliptical motions and have advanced slightly in the direction of wave propagation.

As waves propagate, the water particles move in circular or elliptical paths. During this motion, there is a gradual forward motion of particles, which leads to mass transport. Although individual particles return to their original positions, the overall effect is that mass is being transported in the direction of the wave.

Picture holding a group of people in a conga line moving in circles at a dance party. While each person moves around in a circle, they also slowly move forward along with the group. The entire group (mass) moves forward – just like how the water particles in waves collectively advance as the waves propagate.

--