Salt fingers

Above is a computer simulation of a phenomenon often called salt fingers. They occur in world’s seas and oceans, for example they are common in the Caribbean. Salt fingers form when there is a layer of warm salty water above a layer of colder but less salty water. The point is that salty water is denser than less salty water, so typically a layer of salt water on top of a layer of fresher water is unstable, the denser layer on top falls down through the less dense layer below due to gravity — this is convection. However, here the water on top is not just saltier it is also warmer. This temperature difference works in the opposite direction to the difference in the amount of salt. Warmer water is less dense that cold water and so a layer of warm water floats on a layer of colder water.

For salt fingers, you start from a situation in which the temperature difference wins, in the sense that the layer on top is actually less dense than the layer below. You might think then that the situation is stable, but as you can see from the movie above, it is not.

The reason is that heat diffuses about a hundred times faster than salt diffuses. Think about what happens if by chance a little downward bulge forms in the top layer of hot salty water. As heat diffuses so much faster, this bulge cools very rapidly by losing heat to the surrounding cold water, while its salt concentration only drops a little bit in the same time. But then this bulge is almost as cold as the surrounding cold water, and still has a higher salt concentration. This higher salt concentration makes it denser than the surrounding water, and so it falls under gravity, forming a salt finger.

Salt fingers are very pretty and are one way the water in our planet’s seas mix. They are also, I think, a cute piece of physics. We don’t often worry about which moves faster, molecules or heat, but in fact one moves a hundred times faster than another, and this has consequences. One of these is salt fingers, the other is that when we add sugar* to coffee or tea, we really do want to stir it. If we rely on diffusion, our tea will be cold long before the sugar is mixed in.

* Sugar diffuses a bit slower than salt.