# Fun with fluids: ocean mixing and hot chocolate

Ever wondered how are the cold Southern Ocean and a hot chocolate similar? (credit C. Heuzé)

As my niece just turned 8 and is incredibly curious about sciences, I thought I’d design some basic and fun experiments to introduce her to my research area and interest: oceanography! Unfortunately, fluid mechanics equations are as sexy as a dead pigeon, and I quickly get confusing when explaining the processes with my hands, so instead I turned to our common passion: food! Today, I will introduce the basics of ocean mixing using hot chocolate.

1) Density driven vertical mixing

I would be happy if the only part she remembers is this one, as this is my main area of research at the moment.

In the real ocean, deep water formation is at the core of the whole global circulation. Dense water formed at the surface in contact with the ice sinks vertically to the bottom of the ocean, and then travels equatorward where it will eventually upwell. In real life, using density differences is the most effective way to cool your beverage.

In the ocean, density depends on two parameters, salinity and temperature: the colder and the saltier, the denser. For our chocolate, we will only care about temperature.

In the real world, strong heat transfer to the atmosphere at high latitudes will cool the ocean. That causes the surface to become colder (hence denser) than the underlying waters, making in sink. This sinking in turn forces relatively warmer waters to go to the surface, creating a nice convection cell. In real life, prepare a hot chocolate with boiling water and add cold milk on top: the cold milk, denser, will sink and cause hot water to go the surface, creating a nice convection cell and eddies (see Figure 1 for a coffee example) to homogenise the temperature of your beverage. In practice, temperature mixing is enhanced by the action of pouring milk, unless you put the milk on top very delicately.

Figure 1: Mixing between cold milk and hot coffee: too rapid a phenomenon to be captured by my camera

2) Wind-driven mixing and Ekman pumping

For a long time, wind-driven mixing was the only ocean mixing considered as important, and poor oceanography students still have to learn how to demonstrate the theory of the Ekman spiral.

Basically, the whole ocean moves westward due to the rotation of the Earth (that’s the Coriolis force). When the wind blows it affects the surface of the ocean and makes it move in another direction, but also the subsurface throughout what is called the Ekman layer. Vagn Walfrid Ekman was a Swedish oceanographer who explained why icebergs drift at 90° compared with the direction of wind thanks to the Ekman transport, developed the Ekman current meter and the Ekman water bottle, and played the Ekman piano. In real life, if you blow on your hot drink in one direction while moving your mug in another direction, you should create some motion in the fluid over a depth of a few centimetres. But I doubt you will do that.

On smaller scales, in the real ocean, wind and pressure systems will affect the ocean locally, causing upwelling or downwelling. These upwelling or downwelling are vertical movements inducing differences in buoyancy, so we come back to the previous section. In real life, if you don’t really want to blow cyclonic winds to your cup, you can simulate the action of the winds using a spoon and stirring the hot chocolate.

3) Sea ice: a barrier between the ocean and the atmosphere

Often neglected but key for our climate, sea ice is not only important for its albedo and the polar bears: it also isolates the ocean from the atmosphere.

In the real ocean, at high latitudes, the atmosphere can easily reach -40°C during winter, while liquid sea water is no colder than -1.8°C (salt lowers the freezing point of water). In real life, my kitchen atmosphere is about 22°C and my hot beverage must be around 70°C when I just prepared it.

In the ocean, sea water freezes at the surface of the ocean when it drops below -1.8°C, forming sea ice. In the beverage world, I love covering my hot chocolate in mini marshmallows. These marshmallows melt quite quickly, creating a thick layer on top of my chocolate, as you can see in Figure 2.

Figure 2: Melting marshmallows create a thick insulating layer between your ocean and your atmosphere

In the polar oceans, this layer of frozen water stops heat transfer from the ocean to the atmosphere, so the ocean remains relatively warm compared to the polar atmosphere. In real life, the layer of marshmallows stops heat transfer from my mug to the relatively cooler atmosphere. That prevents my hot chocolate to cool down too quickly but results in me burning my tongue every time.

… I really want a hot chocolate now!

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#### Céline Heuzé

I finished my PhD in physical oceanography at UEA (UK) in March and am now based at the University of Gothenburg (Sweden) for a research fellowship. I'm also a crazy cheese eater and amateur philologist. Interested in all deep, polar waters, outreach, and fun sciency news. I'm co-webmastering SciSnack, contact me if there is a problem.

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