Turbulent times: a dive with sharks

We are taking a look back at stories from Cosmos Magazine in print. In December 2020, fluid mechanist Sophie Calabretto wrote how a shark’s most amazing characteristic is only skin deep.

For as long as I can remember, I’ve loved sharks. By that I mean I’ve loved the idea of sharks, of course, having fallen victim to an older brother who (I can only presume) took much delight in showing me Jaws when I was far too young. In practice, I am sure if I actually saw a shark in the wild, this fascination and awe would quickly dissolve into absolute terror, though with awe remaining. It is for this reason, perhaps, that I have not yet been shark cage-diving. I can imagine it now …

Watching in earnest as a dark, sinister form appears in the distance. I gasp, respirator falling out of my mouth. But I am not paying attention, because there is a SHARK materialising right in front of me. Having forgotten about the respirator, I take a deep breath to calm my nerves, asphyxiate and die.

My dream is to see a shark while I am kayaking out in Sydney Harbour. I will let you know when it is time to eat my words.

The first job I can remember wanting to do was marine biologist and this was predominantly to do with how cool I thought blue-ringed octopuses were, and how amazing and vaguely terrifying I found sharks. I clearly bungled something along the way, however, and ended up as an applied mathematician, using mathematics to understand, explain and solve real-world problems. In particular, I developed a penchant for all things fluid, and so I became a fluid mechanist as well. However, not all is lost: if my education has taught me anything, it’s that sharks live in water and water is a fluid.

Water is a fluid, but so is air, and blood, and honey. Saliva, toothpaste, neon, Jupiter – I think (note from Alan Duffy: Yep, Jupiter is a fluid..! You see beautiful examples of fluid mechanics with the separation of bands, jet streams and the like.) – all fluids. As is anything else that flows. In fact, we’re surrounded by fluids every day and yet we still don’t fully understand why they behave the way they do sometimes. Enter the fluid mechanist. My primary interest is understanding this whole turbulence thing: why fluid goes from moving in a “nice”, laminar way before it gets a little unstable and then transitions into a messy, turbulent flow regime.

Turbulence is fluid behaving chaotically (mathematical chaos, I mean – think Jeff Goldblum in Jurassic Park talking about butterflies) and we cannot predict chaos, which means we cannot predict turbulence. If we cannot predict it, we cannot control it. And yet, sharks seem to have, somewhat, sorted this out.

Unless you’re a drifter, in order to move through any fluid – water or air – you need to create more propulsive force (or “thrust”) than the resistive force (or “drag”) you are experiencing (according to Newton’s Laws of Motion). These resistive forces are then made up of two different kinds of forces: inertial forces associated with the motion of the mass of fluid, and the viscous forces that result from adjacent layers of fluid trying to move over each other. You experience different versions of this every day. It is harder to walk into a strong headwind than no wind at all, because your inertia wants you to move forwards but the headwind’s inertia wants to push you backwards, and it is why hippos (and humans, for that matter) can run faster on land than underwater (since air is less viscous than water, it is easier to overcome the viscous forces).

When we swim, we kick our legs (perhaps wildly, depending on how much time we spent at the beach as children) to push ourselves off from the water behind us, and we use our arms to pull ourselves towards the water in front of us. In comparison, sharks and other aquatic animals have clearly spent a fair hunk of time evolving into pretty impressive swimmers. And that is without ever having had Newton’s Laws explained to them.

Flagellates, like sperm and some bacteria, use flagella (wee, whip-like appendages) to propel themselves by beating the flagella from side-to-side or in a helical motion to create forward thrust. There are paddling swimmers, such as some crustaceans, that use legs or even antennae for swimming (a bit like us, but better). Many cephalopods, including my favourite blue-ringed octopus pals, use a form of jet propulsion, in which they fill a muscular cavity with water and then squirt it out to propel themselves in the opposite direction of the ejected water. (Just like a jet engine that uses water rather than gas… which you now know is also a fluid.)

Sea turtles, penguins and sea lions use their pectoral flippers to propel themselves through the water, and tardigrades just swim like small, weird dogs with eight legs. Some invertebrates, like worms, will undulate their bodies to create propulsion – not unlike sea snakes, which have the added benefit of a paddle-like tail for a little extra kick. Many fish often use this rippling technique, undulating their bodies or oscillating their fins.

 Sharks, aka Monarchs of all Fish or Cheetahs of the Ocean (note to reader: neither of these appellations are, yet, endorsed by the wider scientific community), have incredibly strong fins, which create dynamic lift and propel them forward. Actually, this is a bit of a generalisation: there are more than 500 species of sharks, and I wouldn’t refer to a wobbegong as a Cheetah of the ocean, regardless of the spots.

 I’m thinking about those sharks with more torpedo-shaped heads, like the great white that will cause me to asphyxiate in a cage at some stage in the future. These sharks use their tail, or caudal fin, to propel themselves forward, pushing water around their pectoral fins, which they can tilt up and down in order to create positive or negative lift to move up and down. Along with their vertical fins, which allow the sharks to move from side to side, this arrangement gives sharks incredible manoeuvrability – equivalent to a car (approximately equal to one shark mass) performing a U-turn in your living room.

However, there is something else that is quite remarkable about a shark and the way it interacts with the surrounding fluid. To understand what that is, we only need to go skin-deep. Fast-swimming sharks have skin made up of millions of tiny, tooth-shaped scales known as dermal denticles or placoid scales. These denticles allow a shark to do something fluid mechanists around the world struggle to achieve: they reduce drag in turbulent-flow regimes.

When fluid flows around an object, at a molecular level the fluid immediately adjacent to the object tends to adhere to the surface rather than slip over it. In fluid dynamics, because we are extremely creative, we call this the “no-slip boundary condition”. Fluid flows in layers, so the next (molecular) layer of fluid will move at almost the same speed as the adhered layer, but it will also be influenced by the next layer, which in turn will be influenced by the next, and this happens again and again until we reach a layer that is moving at almost the speed of the surrounding fluid (the “free stream velocity”).

The result of this is a thin layer of fluid in which the velocity rapidly changes from that of the object to the free stream velocity. In fluid mechanics we call this layer a “boundary layer”, and the thickness of the boundary layer will depend on the viscosity of the fluid, with more viscous fluids giving way to thicker boundary layers than less viscous fluids. If I were to spin around in a vat of honey, the honey boundary layer that formed on me (“the object”) would be thicker than the boundary layer formed if I were to spin around in a vat of water. Both of these boundary layers would be thicker, however, than a boundary layer of gin. Boundary layers occur when any viscous fluid (all those fluids we talked about earlier) encounters a solid object or boundary, which is basically everywhere.

When a boundary layer is nicely behaved and flowing in layers, as it should, it’s called laminar. If a boundary layer becomes unstable, however – which it often can in fast-flowing fluid, such as the water passing over a shark hooning around the ocean – the layer can detach from the surface of the object. This detachment point is called the separation point. If it detaches, this layer will encounter the fast-moving fluid, forming streamwise vortices that will become turbulent, creating a ‘turbulent wake’ behind the object, which then causes drag. This is exactly what we do not want to see happening on the surface of an aeroplane: more drag means increased noise and energy dissipation, making planes less fuel efficient and compromising control.

Sharks have curtailed this conundrum. The gaps between their dermal denticles essentially provide microscopic pockets in which these separated vortices can wreak their swirling havoc, allowing the fast-moving fluid to flow straight over the top, reducing the overall drag. This is why there are dimples on a golf ball: forcing the formation of tiny vortices (and, thus, a thin turbulent boundary layer) decreases the size of the wake and minimises the drag felt by the ball. The movement of a shark is (slightly) more complicated than a golf ball’s, but the physics is essentially the same. (Some sharks have circumvented the whole moving-fast-induces-turbulence problem altogether. Epaulette sharks have evolved two sets of flat, paired fins that they use to walk along the sandy seabed. They can swim too, of course, but when they do it, it is on their terms.)

Fin-feet or no fin-feet, one thing is for certain: turbulence occurs in almost every situation that fluid flows. Turbulence occurs at every scale, from the tiny, vortex structures between a shark’s dermal denticles, to the milk in your morning coffee, to the swirls and eddies in a fast-flowing river, to the boundaries of jet streams in Earth’s atmospheres, to coronal mass ejections from the plasma surrounding the sun. If we could understand how and why it occurs, we could do a whole gamut of useful things, such as improving the reliability of and reducing the risk associated with alternative energy, such as wind and tidal. Or better understanding and modelling the “turbulent flow of people” – crowds, influxes of large groups, and mass migration.

 We would also get better at mixing things more efficiently, which is important in both big industrial process engineering applications and the subtle art of Milo preparation. And we will be able to design better aeroplanes, much faster and more fuel efficient than anything previous (like the Concorde if it were not noisy, and didn’t have hugely inefficient engines nor wings designed for supersonic cruising that were not particularly efficient during take-off, landing and subsonic flight).

 But, as noted before, transient turbulence is pretty complicated. So, as we continue to chip away at this (still unsolved) grand challenge of fluid physics, we can continue to learn from the animal kingdom, whose millennia of evolution make them better than us at mostly everything. Except for Bruce, the mechanical shark from Jaws, who never had dermal denticles and, as a result, has since gone into retirement.