1.3. Deep Water and Shallow Water Relations

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. So, the average energy flux per unit wave crest with transmitted across the plane perpendicular to the wave advances is wave power. And it is given as e into CG. This is important CG is group velocity and e is the energy that we just derived. So, the power is given as e into CG or in if you want to write it in terms of celerity. It is e bar n into CG.

Wave energy flux refers to how much energy is moving through a specific area over a certain time period as waves travel. Imagine waves moving through the ocean; they carry energy along with them. This energy flux helps to calculate wave power, which is the total energy transmitted by the wave per unit length of wave crest. The relationship can be expressed mathematically as 'Power = Energy (e) x Group Velocity (CG)'. In simpler terms, if you know how much energy is in the waves and how fast the waves are moving (their group velocity), you can determine the power of the waves.

Think of wave energy flux like a river flowing. If the river (wave energy) flows faster (higher group velocity), more water (energy) reaches a certain point (area) in less time, creating a larger volume at that location (higher power).

For deep water you know that CG was half c not. n = half so, power is going to be half into C not for shallow water it will e into CG because CG is C only if you assume that the wave propagates from deep water towards the shore...

In deep water, the group velocity (CG) is half the wave speed (C0). This relationship is crucial when analyzing how waves behave differently in deep water compared to shallow water. When waves transition from deep to shallow water, their speed and energy characteristics change. For shallow water, the group velocity equals the wave speed. Therefore, when analyzing wave power from deep to shallow water, the equations consider these differences to conserve wave power.

Imagine riding a bike on a smooth road versus riding on a sandy beach. On the smooth road (deep water), you move fast and smoothly due to less resistance, while on sand (shallow water), your speed decreases due to increased resistance. Similarly, waves behave differently in deep and shallow conditions because of these opposing forces.

Because you see this if there is no loss, it is average energy flux per unit wave crest rate. And if we apply the conservation of wave power. So, you see this is any depth...

Wave power conservation means that as waves move from one depth to another, the total energy transmitted by the wave remains constant, assuming no energy is lost. This principle allows us to equate the power at deep water conditions with that of shallow water conditions using specific formulas that account for wave height and speed at both depths.

Think of a water balloon. If you push the water from one end to another without any leaks, the amount of water (energy) stays the same even if you change the shape of the balloon (depth). Similarly, the power of the waves remains the same despite changing conditions as they move towards shore.

So, in deep water, it will be gamma h not squared by 8 h not indicates the wave height in deep water... obtained relationship between the water velocities and only kinematics...

Shoaling refers to the phenomenon where wave heights increase as waves approach shallower waters. The wave height transformation is quantified using a shoaling coefficient (Ks), which relates the deep water wave height (h0) to the height at any shallower depth (h). This transformation allows us to calculate how waves will behave as they move from deep to shallow water.

Picture a car going downhill into a valley; as it descends, it speeds up (waves increase in height) before reaching flatter ground. In a similar way, waves grow taller and more powerful as they enter shallower water.

So, the mass transport velocity is given by phi h by L whole squared into C by 2 cos h2kd + z divided by sin h squared kd...

Mass transport during wave motion refers to the actual movement of particles or water in the direction of wave travel. As waves pass, water particles follow an orbital motion, resulting in a net forward displacement. The mass transport speed will vary based on the wave height and steepness, with higher waves causing greater transport, while longer waves lead to less transport.

Consider a group of kids on a merry-go-round (wave motion). When they push harder (larger wave height), they move forward more quickly when the merry-go-round spins. If they are moving slowly (long period waves), their forward motion is minimal. Thus, the wave characteristics dictate how fast the mass moves.

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