Modest, let me, and this is not to be taken as a hostile action or anything of that matter, reflect back on your post.
You say that it depends on the amount of gases dissolved in the water, however, as i have said before, the cool water can have the same level of gas absorbed in it as the hot water, the fact that the hot water is not boiling, keeps the levels about equal throughout the experiment. You could also used freshly-made distilled water, one that will not have any gas dissolved in it, and the experiment would still turn in favor of the warm water
If you think of it temperature-wise, it really does not make sense, but, if you think of it in terms of energy, and steam, the picture starts to become clearer. Then take into acount the convection currents, that distribute the chilled water on top, to the bottom, perhaps if the top of the water is infact brought down to a lower temperature, but the rest of the mass of water is still fairly warm, you will have convection currents going, even though, the water leaving the top is colder then the water on top of the cold-water comparison. Mind you the water is only said to freeze at 0 degrees C, in reality, much of the body of water gets super-cooled prior to freezing, storing enough energy to turn to ice (and that takes a lot of energy, less, though, then turning the water to steam).
Then you think about the colder water, as a body that will cool fairly uniformly, and when it reaches 4 degrees C, the convection flows will stop, and the colder water will stay at the top, such are the density properties of this weird liquid.
The other thing is heat, may change the surrounding "microclimate" of the area around the glass, releasing more heat, will in term cool the water more. Also there may be consideration of water vapor forming on the outside of the glass, that may aid the thermal bond of the glass to the shelf it stands on, thus once again, drawing out more energy, leading to shorter freeze times.
But this is in line of questions like "can you boil water, using a burner and a single piece of paper, or a plastic bottle" and so forth, i'll try to come up with more
~ Sun, number 1 cause of global warming.
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