Monday, July 14, 2003

Boat wakes mad science:

Asked by Lonnie, a science grad student at Virginia Commonwealth University: When flying I often see the trails of where boats have passed. These are obviously not wakes. They generally appear as a lighter colored path showing where the boat travelled. What causes this anomaly in the water's surface appearance?

They actually are wakes. I know exactly what you mean, because I have wondered about them too ? they aren?t the wave trains we?re used to that water skiers jump over, but much longer features trailing many kilometers behind.

Here are some images of ship wakes taken from the Space Shuttle, which include examples of what you are interested in.

It turns out that wakes are pretty complicated things. In fact, this particular type of feature is not yet fully understood, because most dynamical solutions damp out to a level that should be unobservable this far downstream from the ship. What you are seeing is probably a non-linear interaction between some of the wake features I talk about below.

Being able to see these features requires a special combination of circumstances. First, the state of the sea itself has to be calm enough so that this feature is not swamped out. Second, the lighting angle has to be right. Notice in all the photos in the NASA link above that nearly all the wake features are most visible near the point of maximum reflection of the sun ? since the sea provides a specular surface, the reflection of the sun is ?smeared out? over a wide area, providing brilliant illumination that allows you to see very fine details and differences in the sea state (things like eddies, wakes, squalls, etc.). Third, the ship has to be going the right speed, and passing over the right kind of water for non-linear effects to appear.

A ship?s wake is composed of many different phenomena:

1. The familiar set of spreading waves in a 19.5 degree angle V behind any ship is called the ?Kelvin wake? after Lord Kelvin, who gave the first rigorous description of it. There are actually a set of waves which cross the V too. These waves are what eat up most of a ship?s energy. These wakes are long-lasting, and far reaching. There are some fantastic pictures of Kelvin wakes here.

A lot of research has gone into how to reduce this wake and the energy it drains from a ship ? one result was that you can reduce the transverse waves in the set (and the energy required to produce them) by putting a big bulbous part on the bow of the ship. But unfortunately, only at a particular speed. Here?s an interesting page on hull shapes and how they affect drag on ships.

2. The ?turbulent wake? is all the white foam kicked up by the propeller wash/cavitation and the chaotic eddy shedding at the stern. This wake tends to wash out the Kelvin waves that cross perpendicular to the direction of travel. Here?s a picture of the turbulent wake caused by an aircraft carrier. Since it?s turbulent, it tends to damp out pretty quickly.

3. The ?dead water? wake or ?narrow-V? wake, which looks like the ship flattened out the waves. This wake is also always present, but is very hard to observe, since it?s flat! Turning ships often give a good view of it, and here?s a biggie.This is a big part of what you are seeing, but this wake alone cannot last as long as several kilometers.

4. All of the above are really the surface manifestations of what is really a 3-dimensional process ? all of these wakes have a portion below the surface that is just as complex. One of the large parts of the sub-surface wake is a set of twin vortices that are shed from the stern. They are very hard to see in water, but a parallel type of phenomenon is easily observed in airplane wakes, here.

5. Now we get to the weird stuff. At certain speeds, ships can set up long solitary waves (solitons) that precede the ship. You can think of them as the ?draw-down? before the Kelvin wake comes crashing in. If you want to read some more about these, go get this PDF file.

6. The next complication is the structure of the water itself. As you probably know, very often water is stratified in layers of different temperature, salinity, turbidity, etc. This creates conditions where waves can diffract and reflect internally in these layers making all sorts of complicated effects. These can be classed as ?internal wave wakes.? In some cases, if there is a layer of material (oil, say) on the top surface, this disrupts surface tension forces that cause certain wave/wake phenomena ? these are the ?oil slicks? which are generally flatter than surrounding waters. A detailed analysis of surfactants and radar returns is here.

As you might imagine, all of these things are of great interest to people who want to know where ships are, and how to track them. Not only the military and the coast guard, but also ship traffic management and companies that are tracking their ships? progress (like express mail services that use GPS to track the whereabouts of vans, trains, etc.). Radar is very good at this, since it reflects really well from metal corners, but also very poorly from the exact features you are asking about. In radar images, what you see is a very bright ship followed by a very dark, long streak. To find out more about radar and ship tracking go here and here.

So..... the long streaks of calm water that reflect the sunlight better than the surrounding water are most probably a complicated non-linear interaction of the narrow-V, the vortices, and some internal wakes that depend on the exact structure of the water column.

I hope this helped, Lonnie!