FEATURE ARTICLE
Internal Tides and the Continental Slope
Curious waves coursing beneath the surface of the sea may shape the margins of the world's landmasses
David Cacchione, Lincoln Pratson
Waves Beneath the Waves
Waves moving along the surface of the sea are easy enough to understand, but how can there be waves within the ocean? The simplest way to grasp this strange concept is first to remember that surface waves are, in fact, traveling along the interface between two fluids: air and water. Now imagine that the upper fluid were a liquid instead of a gas; what would happen? There could still be waves at the interface, but they would act somewhat strangely. If, for example, the upper liquid is only a little bit less dense than the lower one, the waves at the interface would seem to have bizarrely large amplitudes, and, intriguingly, they would appear to move in slow motion. (These same effects can be clearly seen in the little wave tanks sold at novelty stores, usually next to the lava lamps).
Similar interfacial waves exist within the ocean. They often form at the base of what oceanographers call the mixed layer, the topmost stratum of the sea, which, being churned around constantly by the wind and waves, is rather homogenous in its physical properties. Beneath the mixed layer the temperature (and hence the density) of seawater changes abruptly. (Scuba divers are sometimes surprised as they pass from the warmer sunlit surface zone through the base of the mixed layer and into to the much colder waters below.) The base of the mixed layer is usually less than 100 meters deep, and the interfacial waves that form at such modest depths are not relevant to shaping the continental slope, which lies deeper down. The internal waves that influence the continental slope are rather different in that they require no distinct density interface. Rather, they form simply because the water gets gradually denser with depth.
To help understand how internal waves can arise in such situations, you might imagine for a moment tagging a small parcel of seawater in some way, perhaps by filling a balloon with water at some depth in the sea and then allowing it to float freely at that level. What would happen then if you were to lift the balloon upward where the water is less dense? Because the water that fills the balloon is denser than its new surroundings, gravity would pull the balloon back down. But the momentum it gains during descent would make it overshoot its equilibrium po-sition, and the descending balloon would soon find itself surrounded by water that is denser than the water it contains. Up then it would go, continuing this vertical oscillation until friction brought things eventually to rest.
With a mental picture of this bobbing balloon in mind, it is not hard to see how such up-and-down motions could be generated within the ocean. One source of energy for driving these oscillations is the daily tides. Although people normally think of the tides as being responsible for changing sea level, they also cause current to move over the ocean bottom, where the flow sometimes encounters submarine mountains and ridges. Deflected by such topographic obstacles, tidal currents can easily generate up-and-down motions, which propagate away from the source in great waves that share the same 12-hour period as the familiar twice-daily ocean tides. These waves constitute what oceanographers call the semi-diurnal internal tides.
The pioneering Norwegian ocean-ographer (and noted humanitarian) Fridtjof Nansen discovered the first examples of internal waves in the Arctic basin at the end of the 19th century. But not until the 1960s did oceanographers become aware that internal waves (and tides) are ubiquitous, that they contain huge amounts of energy and that they regularly mix ocean water as they slosh along the continental slopes.
It was during that lively decade—a phenomenally influential one for Earth science—that one of us (Cacchione) and his Ph.D. advisors at the Massachusetts Institute of Technology, Carl Wunsch and John Southard, first postulated that internal waves could, over geologic time, act to shape the seafloor. Wunsch, a prominent physical oceanographer, had done calculations predicting that internal waves moving up undersea slopes must cause strong currents along the bottom. But at the time Wunsch's theory needed to be tested under controlled laboratory conditions, something Cacchione did as part of his thesis work.
That exercise required a rectangular tank that simulated the real ocean. Wunsch and Cacchione thus made sure that the water in the tank had an increasing concentration of salt (giving the water increased density) with depth. They then generated a series of internal waves using a mechanical paddle that oscillated back and forth about a horizontal pivot centered in the water. This geometry produced simple internal waves in which horizontal water velocities were maximum at the top and bottom of the tank and zero in the middle. These waves traveled from one end of the tank to the other, where a tilting plastic bottom mimicked the continental slope.
In these experiments, dramatic changes to the internal waves arose over the simulated slope, just as Wunsch's theory had predicted. When the waves encountered the plastic incline, their amplitudes grew, their horizontal wavelengths shortened, and water velocities increased—similar in many ways to what one sees when surface water waves hit the beach. In some instances, the internal waves formed tidal bores (large, turbulent, wall-like waves with abrupt fronts), which traveled upslope and then broke up. These breaking internal waves often caused a great deal of swash and backwash, which in the real ocean would scour the bottom.
With their test tank, Cacchione and Wunsch explored a special "critical" condition in which the energy of the internal waves essentially became trapped in a narrow zone along the inclined floor of the tank. At the time, this phenomenon had not been described theoretically, but with their experimental investigation, Cacchione and Wunsch discovered that under this critical condition, water velocities and internal breaking were greatly intensified along the faux slope, well beyond what they had observed for other experimental runs. In subsequent laboratory experiments, Cacchione and Southard demonstrated that internal waves could resuspend bottom sediment and create sediment ripples. Seeing these effects, Cacchione, Wunsch and Southard proposed that if the critical condition were satisfied along continental slopes in the real ocean, internal waves might well control sedimentation.
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