2. Conclusion and Course Closure

So, now we have studied wave energy. It is very obvious that we study 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 and extending down the entire wave. So, the average energy flux per unit wave crest transmitted across the plane perpendicular to the wave advance is wave power. It is given as e into CG.

Wave energy is a critical topic as it relates to how waves transfer energy as they propagate. The 'wave energy flux' is a measurement of the energy transmitted by waves over time. Specifically, it is defined as the power per unit area flowing in the direction of the wave's movement, calculated at a certain plane that is perpendicular to the wave's direction. The formula for wave power combines two important parameters: 'e,' which represents the energy associated with the wave (derived from previous studies), and 'CG,' which is the group velocity, the speed at which the overall shape of waves moves through the water. Thus, understanding wave power involves recognizing how energy in waves is measured and the factors that influence that energy.

Think of a river flowing downstream. The energy in the river (like the energy in a wave) moves faster or slower depending on how steep the riverbed is. Similarly, wave power relates to how fast and efficiently energy moves through the water, impacting how we can harness that energy using devices like wave energy converters.

The wave power is going to be conserved if the wave moves from one depth to another. Because, you see, if there is no loss, it is average energy flux per unit wave crest rate. And if we apply the conservation of wave power, wave power is going to be conserved. In deep water, it will be gamma h_0 squared by 8 multiplied by CG = C_0 by 2.

The principle of conservation of wave power suggests that the energy compound in waves remains constant as they move from deeper to shallower waters, assuming no energy loss. This means that if we start with a specific amount of energy in deep water, the same amount should theoretically be present in shallower water, albeit with some alterations due to changes in parameters such as water depth. The relationship indicates that parameters like wave height 'h' and the group velocity 'CG' will adjust to maintain conservation. Thus, recognizing this conservation principle is critical in studying and predicting wave behavior as they shift across different depths.

Imagine filling a balloon with air. If you squeeze it gently without popping it, the total amount of air remains the same, but its distribution changes as you reshape the balloon. Similarly, as waves travel from deeper waters to the shore, they might change shape (or height) but retain the same amount of energy overall, important for engineering and marine studies.

This is very important again this represents a phenomena which is called shoaling. And this gives the ratio between wave height at any depth in the shallower waters compared to the deep water wave height.

The term 'shoaling' refers to the process by which waves increase in height as they approach shallower depths. This phenomenon occurs due to conservation laws applying to wave energy; as the water depth decreases, the energy in the wave causes the wave to rise rather than lose energy. Thus, the relationship between the wave height in shallow versus deep water is critical for predicting wave behavior near coastlines and for the design of coastal structures.

Consider a skateboarder approaching the edge of a ramp. As they move towards the edge, they gain height and speed—this is similar to how waves rise as they approach shallower waters. Understanding shoaling helps engineers design better coastlines and waterfront structures.

When waves are in motion, the particles upon completion of each nearly elliptical or circular motion would have advanced a short distance in the direction of propagation of waves. This mass transport is happening in the direction of the progress of the wave.

Mass transport in waves describes the progressive movement of water particles due to wave motion. As waves move, individual water particles trace circular or elliptical paths and, as a result, shift slightly in the direction the wave is travelling. This translates to a net movement of mass in the direction of the wave, which is relevant in terms of how waves can shape coastlines and impact coastal ecosystems.

Think of a floating leaf on the surface of a pond when a stone is dropped in. The leaf's path is affected by the ripples (waves) that move across the water, pushing it along slightly in the direction of the wave action, illustrating how energy can move mass with it.

This was the last topic of hydraulic engineering which we have finished now, and with this I would like to close the lecture and also this course. If you have further doubts, please do contact us and the forum or I will be appearing in some live sessions.

Closing a course often involves summarizing topics covered while encouraging students to reach out for support and continued learning. This final message reinforces the connection between the instructor and the learners, as well as emphasizing the importance of clarifying doubts and seeking knowledge even after formal learning has ended.

It's like finishing a class at school where the teacher reminds students that even though the main lessons are concluding, they are still available for questions and additional support, ensuring that learning continues beyond the classroom.

--