What you Need
To do this experiment you will need:
Two bowls that can hold at least a litre
A boiled kettle
Some food colouring.
What to do
First fill one bowl with cold water, and another with our boiled hot water. Then we just need to let them settle, so put a cover on the hot one to retain the heat and leave them to settle for 5-10 minutes.
Then we add just a little food colouring in each bowl in a nice controlled way. Perhaps by dipping a handle of a teaspoon into the food colouring and then just touch the surface of each bowl of water with it.
Then just watch for a few minutes and see what happens.
What may happen
The food colouring behaved differently in the two bowls:
In the hot bowl it spread far and then dropped down to the bottom.
whereas in the cold water it didn't spread quite as far and then it's dropped down to the bottom. It produced a much more definite shape and stayed more still.
Why does it happen?
There are two possible effects that could cause the food colouring in the hot water to spread out more:
If you looked at all the molecules in the water with a really powerful microscope they would appear to be jiggling around. The hotter they are the more they jiggle around, they will tend to push around any other particles in there too, such as the food colouring. So the hot water should spread the colour out faster than the cold. This process is called diffusion.
Because the hot molecules are jiggling about more they will tend to push each other apart, so you will get fewer molecules in a litre, so hot liquid will be less dense and float on the colder liquid. The liquid on the surface is least well insulated so it will tend to cool down quickest, so the hotter liquid underneath will float up over it. This is called a convection current, and will tend to mix up the food colouring with the water.
Probably convection will be doing all the large scale mixing, and Brownian motion the small scale. Of what you can see convection probably dominates.