By Vladimir Brezina
As kayakers, we are intimately familiar with waves on the surface of the water. But waves produced by the same basic physical mechanism—gravity waves—can form anywhere where a perturbation sets off oscillations in a density-stratified fluid. The surface of the water—an interface between two fluids of different densities, water and air—is just the most familiar location. But essentially similar waves, albeit now internal rather than surface waves, can form deep below in the water, and high above in the air.
In the water
Different water layers may have different densities because of differences in temperature or salinity. At the boundaries between the layers—themoclines and haloclines, respectively—internal waves can form and propagate along the boundary. If there is no sharp boundary and the water density varies continuously, internal waves can still form that, in that case, can propagate in three dimensions.
These internal waves have many of the properties of the familiar surface waves: they can, for instance, break just like waves on a beach. But because of the smaller density differences involved, the internal waves can have much larger amplitudes than surface waves (in deep enough water, amplitudes of a hundred meters or more) and much longer wavelengths. Here are two satellite images of internal ocean waves with wavelengths of kilometers:
NASA Earth Observatory: "This image shows both internal waves and surface waves on the Indian Ocean near the Andaman Islands. The active Barren Island Volcano, part of the Andaman Islands, is shown emitting puffs of steam on the left side of the image. ... Sunlight reflecting off the water’s surface gives it a pale, silvery blue color. The tiny wrinkles running roughly horizontally across the ocean are surface waves. Internal waves paint long diagonal lines across the ocean on the right side of the image." (Photo by NASA)
Internal waves (wavelength about 2 km) which move through the Strait of Gibraltar from the Atlantic Ocean (left) to the Mediterranean Sea (right). In this case, water density differences are due to salinity differences, and perturbation is provided by current flowing through the Strait. (Photo by European Space Agency)
Typically, the internal waves are not felt as waves—as changes in water level—at the surface at all. So how are they visualized in these images? According to NASA’s Earth Observatory,
[a]s internal waves move through the lower layer of the ocean, the lighter water above flows down the crests and sinks into the troughs. This motion bunches surface water over the troughs and stretches it over the crests, creating alternating lines of calm water at the crests and rough water at the troughs.
It is the pattern of calm and rough water that makes the internal wave visible in satellite images. Calm, smooth waters reflect more light directly back to the satellite, resulting in a bright, pale stripe along the length of the internal wave. The rough waters in the trough scatter light in all directions, forming a dark line.
When the surface water layer is shallow enough, such internal waves are also thought to be responsible for the mysterious dead-water effect first described by Fridtjof Nansen:
Fram [Nansen’s ship] appeared to be held back, as if by some mysterious force, and she did not always answer the helm. We made loops in our course, turned sometimes right around, tried all sorts of antics to get clear of it, but to very little purpose.
This happens when the progress of the ship is impeded by subsurface waves—while the surface may be completely calm—that in some cases may even be generated by the movement of the ship itself, as in this simulation (description here):
In the air
Similarly in the air. An initial perturbation such as uplift of an air stream over a mountain range can lead to downstream oscillations where the air repeatedly rises (and cools) and falls (and warms). If the moisture content is right, periodic standing wave clouds form at the crest of each oscillation. Here are a few spectacular examples:
NASA satellite image of a wave cloud forming off of Amsterdam Island (at the apex of the triangle of wave clouds) in the far southern Indian Ocean. (Photo by NASA)
Another satellite image of wave clouds over the ocean. (Photo by NASA)
NASA Earth Observatory: "In the North Sea, air encounters a number of obstacles that create wave patterns. In some cases, as over the Faroe Islands, the wave patterns compliment one another, resulting in a wide swath. But in other cases, the waves created by one island or islet interact with waves created by another. The result is a mishmash of circular waves in a classic interference pattern." (Photo by NASA)
As these examples show, these atmospheric internal waves exhibit classic wave properties such as refraction and interference. And when the waves collide or break, clear-air turbulence may strike those of us flying by…
Everything still seems well-behaved, though, in the following aerial views:
Aerial view of wave clouds (photo from WeatherVortex.com)
Wave clouds over the Sea of Japan. (Photo from WeatherVortex.com)
In sum, as NASA’s Earth Observatory remarks, “If air were visible, it would be a thing of mesmerizing beauty and motion. Air courses in streams and eddies; it rises and falls and flows.” The same goes for the ocean waters. Those motions are there whether we see them or not. And sometimes, indeed, the circumstances are just right to reveal to us, suddenly, this beauty and this motion.
Vladimir Brezina (RIP) 
Johna Till Johnson
Wind Against Current 
Fascinating and beautiful!
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I had never thought of this; very interesting
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Yes… I particularly like the way, once you realize that all this is going on, the idea of waves expands into three dimensions, both below and above you as you paddle along at the two-dimensional air-water interface… :-)
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Hm, the “dead water effect”. I’ve felt it often when paddling. Oh, wait, maybe that’s just getting tired :-).
A lovely piece… which I can say as I had nothing to do with it except read, and enjoy!
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:-) Actually, there is a dead-water effect in kayaking that I’ve definitely felt on occasion. When paddling in very shallow water, the waves generated by the kayak interact with the bottom and slow the kayak down dramatically (see, e.g., Burch’s Fundamentals of Kayak Navigation). The basic mechanism is similar to the one described in this post, but the interaction is with the bottom rather than with a water layer.
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Excellent! Thanks for sharing this.
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Glad you found it useful!
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Masterfully done explanation of an endlessly fascinating topic. Thank you! Now I want to go paddling.
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Thanks, Claire! Yes, having written this post, I think I will have a broader perspective now too when I go paddling!
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A lovely explanation. Do swimmers run into the same problem or are we too small and slow?
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Do swimmers run into the problem of “dead water”? I would think yes, in principle.
But in practice, the top water layer would have to be very shallow. (Then again, that does happen—remember swimming in pleasantly warm surface water while your feet periodically encounter cold water just underneath?)
And yes, the swimmer’s speed might be too low for a significant wave to develop.
But perhaps most importantly, whereas a boat moves along smoothly, allowing a smooth wave to develop and the whole boat-wave system to come to a steady state in which the progress of the boat is continuously impeded, it seems to me that the jerky movements of the swimmer would prevent the establishment of such a steady state…
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Great post, about a topic near to my heart. Check my post on internal waves breaking in the hudson:
I have endless acoustic images of hudson internal waves actually, and maybe I’ll get inspired to post them.
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Thanks Philip! I was not aware of your post—it was before we started blogging—but it fits right in as it shows some of these phenomena right here, in the Hudson! Very cool!
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this was a fascinating read, and really opened my eyes to something I had never seen
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Glad you liked it!
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I really love this kind of “stuff” and thoroughly enjoyed reading this.
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Good to see that somebody is reading the old posts :-)
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I have some catching up to do here. You have categories that are of great interests to me. By the way, I actually saw photographed (poor quality) K-H wave clouds Funny thing, is that I’d just discovered them in my personal studies the day before. Karma.
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Karma indeed!
We’ll try to keep writing faster than you can keep reading ;-) But thanks so much for reading the old posts… I’d almost forgotten this one existed!
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