# Diffusion or turbulence?

## Summary:

Hey! I don't know if this is the right forum to ask this type of question, but I guess "earth sciences" is the closest topic here. So why does a drop of dye in a rotating bucket form vertical columns, but in non-rotating water, it flows out in all directions?
<Mentor moved to Physics>
My teacher talks about turbulence (2D and 3D), but I don't quite understand this. How is the turbulence different in the two buckets, and why does my teacher talk about turbulence but not diffusion? Is not diffusion the reason why the dye spreads in the water? I have searched a lot on the internet, but I don't find any information that explains this in detail. The reason that I'm asking about this in the "earth science" forum, is because it's supposed to be related to the oceans and atmosphere. Again, I'm struggling to see the relation between the ocean and this experiment. I would really appreciate some help, because I'm lost.

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## Answers and Replies

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jim mcnamara
Mentor
Moving to Classical Physics - you will get good answers there

boneh3ad
Science Advisor
Gold Member
I am having trouble visualizing what you mean in the rotating bucket case. Do you have a YouTube video or anything that illustrates what you mean?

Whether "turbulence" or diffusion dominates is likely going to depend on the Atwood number (a dimensionless density ratio) between the dye and the water.

Astronuc
Staff Emeritus
Science Advisor
Summary:: Hey! I don't know if this is the right forum to ask this type of question, but I guess "earth sciences" is the closest topic here. So why does a drop of dye in a rotating bucket form vertical columns, but in non-rotating water, it flows out in all directions?

<Mentor moved to Physics>
My teacher talks about turbulence (2D and 3D), but I don't quite understand this. How is the turbulence different in the two buckets, and why does my teacher talk about turbulence but not diffusion? Is not diffusion the reason why the dye spreads in the water? I have searched a lot on the internet, but I don't find any information that explains this in detail. The reason that I'm asking about this in the "earth science" forum, is because it's supposed to be related to the oceans and atmosphere. Again, I'm struggling to see the relation between the ocean and this experiment. I would really appreciate some help, because I'm lost.
The difference between an ocean and bucket is one of scale. Diffusion (due to concentration gradients) is always occurring in a fluid (gas or liquid) as well as advection (bulk motion), but the effect of advection is dependent on velocity and gradients of energy or momentum. See - https://en.wikipedia.org/wiki/Advection - for a discussion.

In a calm sea with essentially no gradient of density, temperature (thermal energy), diffusion would dominate. With a driving force, such as from wind or waves, or strong gradients, then convection (and turbulence) becomes more important, and at some point, dominant.

In still water in a bucket, the spreading of dye is driven by diffusion, and possibly some convection. W

sophiecentaur, Lnewqban and Kolika28
The difference between an ocean and bucket is one of scale. Diffusion (due to concentration gradients) is always occurring in a fluid (gas or liquid) as well as advection (bulk motion), but the effect of advection is dependent on velocity and gradients of energy or momentum. See - https://en.wikipedia.org/wiki/Advection - for a discussion.

In a calm sea with essentially no gradient of density, temperature (thermal energy), diffusion would dominate. With a driving force, such as from wind or waves, or strong gradients, then convection (and turbulence) becomes more important, and at some point, dominant.

In still water in a bucket, the spreading of dye is driven by diffusion, and possibly some convection. W
Thank you for a great answer!

I am having trouble visualizing what you mean in the rotating bucket case. Do you have a YouTube video or anything that illustrates what you mean?

Whether "turbulence" or diffusion dominates is likely going to depend on the Atwood number (a dimensionless density ratio) between the dye and the water.
It's called DIYnamics. Here is a link to a youtube video

boneh3ad
Science Advisor
Gold Member
It's called DIYnamics. Here is a link to a youtube video
I assume (base don this video) that by "vertical columns" you are referring to the cellular structure they describe in the video?

This is called the Rayleigh-Bénard instability or Rayleigh-Bénard convection. This most commonly occurs with a fluid heated from below but it can also occur with a fluid cooled at the top (as was made clear in the video when it references fluid cooled by evaporation at the surface). You end up with a layer of cooler, denser fluid sitting on top of a layer of warmer, less dense fluid, which is an unstable system. If the "bucket" isn't spinning, then it doesn't set up the same degree of cooling due to the relative motion of the water and air that you get from the rotating bucket case.

Here it is demonstrated on a stove top:

And here it is demonstrated in a lab setup with a rotating column:

Kolika28
I assume (base don this video) that by "vertical columns" you are referring to the cellular structure they describe in the video?

This is called the Rayleigh-Bénard instability or Rayleigh-Bénard convection. This most commonly occurs with a fluid heated from below but it can also occur with a fluid cooled at the top (as was made clear in the video when it references fluid cooled by evaporation at the surface). You end up with a layer of cooler, denser fluid sitting on top of a layer of warmer, less dense fluid, which is an unstable system. If the "bucket" isn't spinning, then it doesn't set up the same degree of cooling due to the relative motion of the water and air that you get from the rotating bucket case.

Here it is demonstrated on a stove top:

And here it is demonstrated in a lab setup with a rotating column:
Ohh, thank you! Really appreciate your help!

boneh3ad
I forgot to ask last time, but why do we add turbulence? Is it a weather phenomenon we are trying to demonstrate?

boneh3ad
Science Advisor
Gold Member
What do you mean "add turbulence?" Turbulence is a naturally-occurring phenomenon. It happens on its own as long as conditions are met for its development. We don't need to add anything.

What do you mean "add turbulence?" Turbulence is a naturally-occurring phenomenon. It happens on its own as long as conditions are met for its development. We don't need to add anything.
Ups, I'm sorry for the confusion. I forgot to mention something. In the experiment we also studied what would happen if we stirred (added turbulence) to the rotating water before adding dye. We then saw these vertical curtain wrapping around each other, still some sort of 2D motion. From the top of the bucket it looked like swirls. And then comes the question I asked at last:
I forgot to ask last time, but why do we add turbulence? Is it a weather phenomenon we are trying to demonstrate?