As the Whale Turns

The shape of the humpback’s flippers might hold the secret to more maneuverable submarines.

whale in bubble net

Humpback whale attacks its prey by encircling them in a "bubble net"—a turbulent cylinder of bubbles the whale creates by expelling air through its blowhole as it spirals upward toward the ocean surface. The path of the whale has been traced for clarity by a series of columns of bubbles. The bubble net can be as small as five feet in diameter. Such tight turning is made possible by the hydrodynamic lift generated by the whale’s long pectoral flippers.

Patricia J. Wynne

The humpback whale, that mighty leviathan of the briny deep, hardly strikes one as a marvel of agility; on the contrary, it seems the very embodiment of stateliness and power. Each the size of a school bus, these awesome mammals cruise, mouths agape, so as to gather the tons of biomass they need to sate their appetites every day.

But the humpback gives the lie to the notion that things of great bulk move only by lumbering. After all, who hasn’t seen, at least on film, the spectacle of a huge whale’s great breach, its breathtaking leap from the water followed by a great returning splash? And underwater, the animals move with such astonishing agility that they’ve caught the attention of naval engineers, who hope that some of the principles learned from the study of the humpback’s flippers can be applied to designing submersible vehicles of unprecedented maneuverability.

Megaptera novaeangliae, the humpback’s scientific name, means “big-winged New Englander”—a nod to the pods of humpies living near the Stellwagen Banks of Massachusetts Bay, as well as to their very long flippers. Humpbacks, like other baleen whales, eat large amounts of small prey. But instead of simply swimming through aggregations of prey, as many of their cousins do, humpbacks often make “bubble nets”—narrow, cylindrical walls of bubbles—by exhaling while they swim in circles beneath their prey. The bubble nets concentrate the prey, and so, when a whale then swims through the center of a bubble net, its payoff is a rich mouthful.

Bubble nets vary in size, depending on the kind of prey the whales are pursuing. When a humpback is corralling herring and other fishes, the net may be 150 feet wide. But when the humpbacks are rounding up krill—small, shrimpy crustaceans—the net may be as small as five feet across. That behavior raises an intriguing question: How can a thirty-five-foot-long animal swim in such tight circles?

The question has long fascinated the aptly named Frank E. Fish, a biomechanist at West Chester University of Pennsylvania. Fish thought the secret to the humpback’s tight turning radius might be its flippers. The humpback has the longest flippers of any whale, and they lie substantially forward of the whale’s center of mass, well placed to exert turning forces on the whale. In fact, the two flippers look quite a bit like wings: each is between nine and twelve feet long, about four times longer than its width, and each has a rounded leading edge and a thin trailing edge. Most intriguing, each flipper also has large bumps, called tubercles, that jut out from its leading edge, giving the flipper a serrated appearance.

Over the years, biologists have suggested a number of possible functions for the humpback’s flippers. Some have seen them as large heat exchangers, or prey attractors, or devices for making sound when slapped against the water. Some have seen them as hydrofoils—water wings—that help the whale make its turns. Oddly, the tubercles have not led to the same level of speculation.

Working with three engineers—David S. Miklosovic and Mark M. Murray, both at the U.S. Naval Academy in Annapolis, Maryland, and Laurens E. Howle of Duke University in Durham, North Carolina—Fish set out to test his hypothesis that the tubercles help the flipper hydrodynamically. For their work, the four investigators relied on two scaled-down plastic replicas of a humpback flipper, twenty-two inches long. One replica featured prominent tubercles; the other had the same area and cross section, but a smooth leading edge. Both models were then tested in a wind tunnel.

A wind tunnel might not seem to be the environment of choice for testing a flipper that functions in water. Fortunately, though, results obtained with airfoils in moving air can be “translated” into findings that pertain to flippers moving in water. The key to the translation is known as the Reynolds number, a kind of scaling factor that combines three sets of numbers to summarize how an object interacts with a surrounding fluid. In this case, the sets of numbers relevant to the Reynolds number are the length and width of the wing, the density and viscosity of the surrounding fluid, and the speed at which fluid and fin slide past each other.

As long as the Reynolds number is held constant, a one-hundredth scale model of an airplane wing will act just like its full-scale version—and a scale model of a flipper in a wind tunnel can become a stand-in for the real thing in the ocean. That remarkable property is a huge convenience for engineers and biomechanists, making it possible to study objects moving at practical speeds simply by varying the viscosity of the surrounding fluid. In this case, Miklosovic and Murray kept the Reynolds number for their scale models appropriate to conditions in nature by running the air past the models faster than the whales would move in seawater. Yet they were still able to get a good idea of the effect of having bumps on the leading edge.

wing

Fluid—whether liquid or gaseous—passing over a wing (blue arrows) creates lift (upward-pointing arrow). But what distinguishes the humpback’s flipper from an ordinary wing is the presence of tubercles, or bumps, on the flipper’s leading edge (above left). The tubercles enable the flipper to create lift at angles as steep as roughly seventeen degrees, because the water gets accelerated into an organized, rotating flow behind the troughs formed by the tubercles. A flipper with a smooth leading edge (above right) would stall, or cease to provide lift, at such an angle, because the water would be spun into a disorganized series of eddies.

Patricia J. Wynne
The body of a whale is relatively stiff, and so the animal cannot curve sinuously into a turn the way a swimming seal can. To propel itself around a corner, a whale instead relies on the lift generated by its flippers. Fish and his colleagues found that the tubercles enable a flipper to continue generating lift at angles of attack 40 percent steeper than are possible with a smooth wing [see illustration above]. In other words, when a humpback turns, it can roll farther onto its side without losing its “grip” on the water, and so make a sharper turn, because of the tubercles.

But the tubercles would seem to solve one problem only to introduce another. Protruding into the flow as they do, they would appear to increase the drag of the flipper as the whale swings into a turn. Appearances can be deceiving, though—particularly where drag is concerned. When the scalloped flipper is held nearly horizontal in the flow, the drag is no different from that of a smooth flipper, and at high angles of attack the drag is actually lower. So, just when the whale is using its flipper to turn the tightest, the flipper slides through water more easily than it would if it had a smooth leading edge, even as it generates far more lift than a smooth flipper could.

With their stiff bodies, whales are far better analogues for man-made submersibles than more sinuous aquatic animals are. Fish and his colleagues hope to design guidance fins for underwater vehicles that can give them some of the agility that enables a thirty-ton animal to turn on a dime—or at least a large doormat.

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