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INTERNAL WAVES

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The opening sentences of Chapter One described waves as undulating forms that can travel on the interface between any two fluids of different density. The surface of the sea is the obvious place to study waves; however, other waves that are quite different in character travel on the interface between layers of slightly different densities within the ocean. These are internal waves. Imagine pulling a parcel of water down into more dense water, then letting it go; it will rise because it is less dense than its surrounding water. But when it has risen enough to be neutrally buoyant, it continues to move as its inertia causes it to rise into less-dense water. When its upward motion stops, it sinks back downward. This repeating process is the essence of internal wave motions. It is similar to a hanging weight oscillating on a spring where the buoyant force is represented by the spring. Because waves are driven by gravity, it follows that if there is a substantial difference between the densities, as there is between air and water, the forces that tend to restore a flat surface are great. If the density difference is small, as it is between layers within the ocean, the restoring forces are much weaker. The period at which an internal wave will oscillate is related to the water’s density gradient (stratification) and is called the Brunt–Väisälä frequency, or buoyancy frequency, N. N equals the square root of gravity divided by the water density of the parcel multiplied with the change in water density divided by the change in depth.


A larger value of N indicates a more stable (stratified) water column. This is important in the real world when less-dense river water flows into the ocean and when glaciers and sea ice melt. Waves are always working, mixing nutrients and dispersing pollutants, even while massaging sediments below. All are affected by gravity, buoyancy, and ocean stratification.

The wave periods, lengths, and heights of internal waves can be very much greater than those of surface waves. Although the heights may be large—over 330 feet (100 m or more)—the energy these waves contain is smaller than surface waves and the typical velocity is low, averaging less than 1 foot per second (30 cm/sec).

It is not essential to have an abrupt density interface; any stable density stratification can support internal waves. And because there is usually a relatively warm surface layer over much of the ocean, internal waves are a common phenomenon. Although the major part of these waves is well below the surface, evidence that they exist can often be seen, especially on calm, clear days. This is because internal wave currents affect the reflectivity of the sea surface by producing alternating bands of slicks and (small-scale) roughness.

Internal waves are important in several ocean processes. For example, the cold, dense water formed in polar regions sinks and spreads over the bottom of the ocean basins, and somehow it must be mixed with the waters above if a reasonably steady state is to be achieved. Internal waves are a significant cause of this mixing, and they may play an even greater role in the transfer of momentum, especially between layers of water that are moving in different directions. The intermittent mixing and uplift of phytoplankton (tiny plants that are the foundation of the oceanic food web) into the sunlit surface water by the passage of internal wave crests leads to increased biological productivity. The power continually dissipated by internal waves is immense and has been calculated to be as large as the power used by humans on Earth; some estimates are over 2 terawatts continuously, for all 8,736 hours per year (or 17,000 terawatt hours per year).

Internal waves are generated by the addition of downward energy from external sources. In principle, they can be set in motion by moving atmospheric pressure fields (i.e., weather fronts), variable wind stresses, surface waves, tides, ships, and downward-moving or upward-moving currents.

Sensing the presence of these huge, slow-moving waves requires a great many measurements. Researchers from the Scripps Institution of Oceanography recorded shoreward-moving bands of variable roughness by means of a time-lapse camera on a cliff top. A series of temperature versus depth measurements using a towed thermistor (a type of temperature sensor) chain hundreds of feet deep (200 meters deep with a temperature sensor every meter, recording on shipboard) was used extensively by Woods Hole oceanographers in Massachusetts to obtain a reasonably detailed picture of internal waves as revealed by temperature variations. Internal waves are observed almost everywhere when there are fluid layers with different densities.

The Internal Wave Mystery

Internal waves can still confuse researchers. In the early 1990s, I was conducting some autonomous vehicle research in the deep waters off of Bermuda. A vehicle was deployed and programmed to descend to 3,000 feet (1,000 meters), taking sensor measurements along the way, before becoming neutrally buoyant at 3,000 feet (1,000 meters), and then returning to the surface. The vehicle dynamics were well understood, and we could comfortably predict the vehicle mission times with great accuracy. However, our first deployment off Bermuda was a “knuckle-biter” because the time required for the vehicle to return to the surface strangely doubled. We inspected the vehicle for defects, found none, and deployed it for a second time. Again, the vehicle misbehaved. Weeks later, after we examined the data, we solved the mystery. We had not anticipated the vertical movement of the large 330 foot (100 m) internal waves. Our neutrally buoyant vehicle had been “riding” the immense internal waves! We observed similar events in the Pacific with other vehicles. Today, this neutrally buoyant technique is exploited to understand the motion of internal waves and their influence on biology and ocean mixing. All parts of the ocean have their “ups and downs.” – KM

High-frequency underwater sounds make marvelous picture-like acoustic records of internal waves. This is possible because “pings” of sound hundreds of kilohertz from instruments are backscattered by the billions of tiny animals called zooplankton that are concentrated in layers of constant density or temperature. The returning echoes from depths to about 150 feet (50 m) are recorded and, ping by ping, a graphic representation develops of the changing pattern as internal waves pass. A specialized system can detect water turbulence that does not have abundant animal life. An objective of this type of work is to understand ocean mixing and biological productivity. When the tide in summertime comes into Massachusetts Bay, for example, it generates a packet of internal waves as it passes Stellwagen Bank. Sometimes the surface influence of these waves (alternate bands of slick and rough water) can be seen by radar. Over the years, radar has become increasingly useful in detecting the properties and the wave motions of the surface of the ocean. Radar can use radio (electromagnetic) signals from a few MHz to over 100 GHz depending on the phenomena to be observed.

Waves and Beaches

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