Physics of Whales Swimming

Physics of Whales Swimming

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Animals can't rotate like wheels on a car. They must move by oscillatory motion. The resulting flow of fluids are complex and create agonizing studies for biofluid students. These students often find themselves at the forefront on research in fluid dynamics of unsteady, complex viscous flows.

Often men have marveled at the dolphins and whale and at how gracefully they moved through the water. Jim Rohr, a fluid dynamicist working for the US Navy was on an evening cruise in the waters near San Diego when he saw nature doing what scientists had failed to do in the lab: reveal water motion to the naked eye. Watching the plankton bioluminesce as the boat moved by he realized that if he could measure that luminescing he could measure fuid dynamics, turbulence and laminar flow.

But how do the plakton know that the water is moving? And what forces act on animals as they swim?

The answer is mechanical strain of relative motion. Fluids flow around walls slower than they flow in the middle. As the fast molecules tug on the slow ones this creates shear stress. Since velocity is always zero, the faster the liquid, or the animal moving through it, the greater the sheer stress. This is laminar flow. But at some point laminar flow turns to turbulence. Turbulence decreases speed because it increases drag. The plakton were feeling the pull of the drag gainst their cells and luminescing.

Whales create spectacular sights as they cruise through the ocean. We have observed them as they thrust with powerful tails and direct themselves with stiff pectoral flukes. To move forward they swing their tail in vertical motions. This powerful motion can push them for hundreds of miles during migration or jettison them out of the water in amazing aerial displays. Below is an animation of an orca as it moves its tail to go forward. Notice that the front of the body is fairly rigid as a planning surface. Other whales, like the Grey Whale, are more streamline for longer journeys. The gray whale migrates from Alaska to Baja twice a year in the spring and fall.

Rohr believed that bioluminescence could solve a very large question: do whales and dolphins have frictionless skin and can we imitate it?

Laminar flow creates much less shear stress than turbulent flow at the same velocity because there is no swirling or random motion.

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So the intensity of light triggered by a swimming dolphin should reveal the way water flows over their bodies. When Rohr put a dolphin in plankton rich water he found just what he expected. The areas of the body that lit up the brightest were those behind the blowhole and flukes, where there was probably a turbulent wake. The tail half of the body was brighter than the head due to the motion the tail made as it swam. The darkest area was the melon, where the dolphin uses echolocation to find its way, which is an area designed to prevent turbulence.

One way to inperpret these light patterns is that the fluid starts out moving along the body as a laminar flow. As it rushes along the body it becomes increasingly turbulent. It is difficult to calibrate light to a value for turbulence and this is where tests and calculations take over.

As a whale or dolphin moves through liquid it creates turbulence. This turbulence is overcome by streamlining the body. Streamlining is tricking the liquid into following laminar flow.

The streamline is the path of the water around the body of the animal. As it moves it may change the magnitude and direction of the velocity but its vector will always be tangent to the streamline of the body. Streamlines never cross.

So if v = velocity, A = area and t = time then

DV = A1v1Dt

where v1Dt is a small distance. This means that if the speed, v, is constant then the particle will pass any point on the animal such that

A1v1 = A2v2

This can be turned into a generalization for the volume flow rate, r, of the fluid and is called the equation of continuity for fluid flow. It tells us that the flow is faster around linear body parts where the streamlines are closer to the streamlines of the body.

R = Av = a constant.
This is difficult, if not impossible to calculate for whales and dolphins as they move through water because they are not a closed system, like a pipe, but interact with an entire ocean. This is why Rohr used bioluminescence and why scientists continue the study.

Bibliography:

http://ostrich.usc.edu/rsg/gfd/gfd_index.html

Jim Rohr et al. 1998. Experimental approaches towards interpreting dolphin-stimulated bioluminescence. The Journal of Experimental Biology, v. 201, p 1447
Halliday, D., Resnick, R and Walker, J. 1997. Chapter 15 Fluids. Fundamentals of Physics Extended. Fifth Edition.
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