2. Surface Solitary Waves

Now, after the classification, we are going to take our attention to a topic which is related to, you know, open channel. And that is called surface solitary waves. And the prelude to this is, in the definition we had clearly specified that in open channel flow, the free surface can distort. And the smallest distortion can produce waves and that is what we are going to see.

Surface solitary waves occur when the free surface of water in an open channel distorts due to some initial disturbance. The definition indicates that this free surface can change shape, leading to the formation of waves, which are essentially disturbances that travel along the surface of the fluid.

Think of a calm pond where you toss a stone into the water. The point where the stone hits the water causes a small splash, which is similar to a distortion in the water's surface. This creates ripples that move outward from the point of impact, demonstrating how a small disturbance generates waves.

So, this is the free surface, if we push it with something, you know, something like this can be formed and this pattern is called waves. You have you can actually bring, you know, water, I mean, bring some water in a pan or, you know, in a maybe a big kettle and where the or it is exposed to the free surface and you try to push it with one hand, you will see a disturbance at the surface will be there and it will travel.

When a force is applied to the free surface of water, such as pushing down on it with a hand or dropping an object, the water level rises momentarily, causing a disturbance that propagates away from the point of contact. This movement in the water creates waves that can be observed traveling across the surface.

Imagine filling a large bowl with water and gently pushing down on the surface with your fingers. The ripples you see moving outwards from your fingers represent the generated waves, showing how motion on the surface can create a pattern that travels over a distance.

Suppose there is, you know, a water, water enclosed in this area and we have a moving end wall. So, I mean, supporting this water is a moving end wall on one side. So moving end, because if we can move this wall the disturbance can be produced and the waves can be generated.

In a controlled setting, such as a tank with water and one wall that can move, the motion of the wall can create waves. When the wall moves, it pushes the water in the tank, causing a displacement of the water surface, which leads to the generation of waves. This principle can be utilized in experimental setups to study wave behavior.

Consider a wave pool at a water park. When waves are created by a machine that simulates a moving wall, it generates artificial waves that travel across the pool. These waves are similar to what happens in a natural water body, demonstrating how mechanical action can create waves.

Now, if there is any stationary observer, so, as u as any stationary observer, what are you going to observe, you will observe single wave that moves down the channel with a wave speed c, which we do not know now.

An observer that is stationary while a wave moves past will notice that a wave travels at a certain speed (denoted as 'c'). This scenario signifies how waves can be perceived differently depending on the observer's position and motion relative to the water's surface.

Imagine someone standing on the shore of a beach watching the waves come in. They can observe the waves rolling towards them, estimating their speed and height. The experience differs from a surfer who rides the wave, feeling the motion and speed from within the wave itself.

So, for such an observer, the motion is unsteady. The motion is therefore, unsteady for such an observer, who is basically stationary and observing from a distant point.

For a stationary observer watching a wave pass, the flow appears unsteady because it changes over time as the wave moves. In contrast, if an observer moves with the wave at the same speed, they would perceive the flow as steady since the water remains at a consistent point in relation to them.

Think of an observer on a train looking out at a passing landscape. If the train moves fast enough, the scenery appears to be moving past the window rapidly (unsteady), whereas if the observer stands still in a field while watching a train pass (also unsteady), their viewpoint changes little as the train approaches and moves away.

Now, we have much more, you know, science included in this, what we have done, we say that the channel width is b. And we draw the control surface as indicated by this.

Using scientific methods, we can represent wave phenomena mathematically by establishing parameters like channel width and control surfaces. This allows us to analyze the flow rates and behaviors of waves through equations, providing a quantitative view of the physical processes at play.

Consider a water flow related experiment where height measures are taken with a measuring device (i.e., a ruler) to see how much the water rises during a wave. These metrics help better understand the properties of waves and their interactions with the environment.

--