How Can Velocity Measurements Determine Flow Self-Similarity?

[member 428835]

Can someone help me to know by looking at a flow or data of the flow (velocity measurements at specific points) if a flow is self-similar? I'm thinking of something like a vertical jet emitting fluid into a transverse velocity field. But any example works.

Thanks!

 

[Achy47]

As a scientist with expertise in fluid dynamics, I can help you understand how to determine if a flow is self-similar by looking at velocity measurements at specific points.

Self-similarity in fluid flow refers to the similarity of the flow patterns at different scales. This means that the flow at a larger scale is similar to the flow at a smaller scale. To determine if a flow is self-similar, we need to look at the velocity measurements at different points in the flow.

One way to do this is by plotting the velocity measurements at different points along the flow. If the plot shows a similar pattern or trend, then the flow is likely self-similar. However, if the plot shows significant variations or differences, then the flow is not self-similar.

Let's take the example of a vertical jet emitting fluid into a transverse velocity field. In this case, we would take velocity measurements at different points along the vertical jet and plot them to see if there is a similarity in the pattern. If the plot shows a consistent trend, then the flow is self-similar. However, if there are significant variations in the velocity measurements, then the flow is not self-similar.

Another way to determine self-similarity is by using dimensionless parameters such as the Reynolds number. The Reynolds number is a dimensionless number that relates the inertial forces to the viscous forces in a fluid flow. If the Reynolds number is the same at different points in the flow, then the flow is self-similar.

In summary, to determine if a flow is self-similar, we need to look at the velocity measurements at different points and see if there is a consistent pattern or trend. We can also use dimensionless parameters such as the Reynolds number to confirm self-similarity. I hope this helps! Let me know if you have any further questions.