Temperature distribution in a glass of cola with ice

I’ve got a tall glass of cola with ice (I’m using cola because it’s dark). As the ice gradually melts, obviously the water surrounding the ice is colder than the cola at the bottom of the glass. Shouldn’t the cold water sink to the bottom, similar to the interaction of hot and cold air? What I’m seeing is that the water (melted ice) remains at the top, yet the cold temperature does extend downward. Apparently the heat is transferred upward from the bottom, without a lot of mixture going on. What prevents it from mixing?

The heat from the room going into the glass isn’t being used to raise the temperature of the system - it’s being used to melt the ice. Only when that is done will the cola start to get warmer.

cola syrup is denser than water. I imagine if you could somehow force the ice to the bottom of the glass, you’d see much more mixing going on.

Also note that the maximum density of water occurs at 4°C, so if the water on top is colder than this(it’s right next to the ice, so it should be at 0°C), it has no incentive to sink.