Dead Water for Designers

[Chris Ostlind]

I rather like this article

http://www.newscientist.com/channel/fundamentals/dn15003-mysterious-dead-water-effect-caught-on-film.html?feedId=online-news_rss20

It represents some very interesting considerations for designers. One can only wonder how much of this scenario might develop in the North Atalantic if Global Warming continues to pour massive amounts of fresh water down from the Arctic.

Be sure to check out the video clip that goes with the story.

[daiquiri]

Yes, it is really fascinating. And a well-done video. :)
I learned about the Dead Water phenomenon for the first time during a bibliographic research I did few years ago, when I wanted to know more about the shallow-water and blockage effects. Basicaly, I needed to understand why did the velocity tests we performed on one boat yield results so inferior to expected. It all became clear when we turned the echo sounder on. There were only 8 feet of water below the keel. :D
Yeah, I know it has little to do with this one, but the effect is somewhat similar.

[Ike]

Fascinating

[rwatson]

Is this why it is harder to swim in the shallow end of the pool?

[daiquiri]

Is this why it is harder to swim in the shallow end of the pool?
I guess yes - but only if the shallow end is far enough from your start point. :)

The shallow water effect depends on the "depth Froude number", defined as Fnh = V / (g H)^2, where V is the speed, g is gravitational acceleration, H is the water depth. All units must be consistent (i.e., don't mix knots with meters and feet).
The effect of shallow water is negligible for Fnh<0.4. The speed loss will be about 1% for Fnh=0.6, about 4% for Fnh=0.8 and about 14% for Fnh=1.

If your name is Michael Phelps (in which case I would, first of all, like to express you my sincere compliments for the incredible results at the last Olympic Games...) then you are swimming 200 meters in 1'42"96, which gives a speed of 1.94 m/s.
In that case you will have a speed loss bigger than 1% only if the depth of the swimming pool is less than 1.07 meters (3.5 feet). For depths bigger than that, mr. Phelps, you will feel no difference.

If you are just a recreatonal swimmer, than your speed will be something like 1.1 m/s, and you might feel the shallow water effect only in a swimming pool shallower than 20 cm, (7.8 inch). But if you are able to swim in that kind of pool, than your problems with speed are probably more related to the unusual shape of your body. :)

There is a paper at HydroComp site which summarizes this in a crystal-clear way and gives few examples for boat's navigating at common speeds:
http://www.hydrocompinc.com/knowledge/whitepapers/HC124-ShallowWater.pdf

[rwatson]

Hmmm - interesting. I am not much of a swimmer, but it was definitely harder to swim at the 2 metre end than the 10 metre end.

Looks like I will have to to some tank testing. I am suspecting my poor kicking technique with my big feet being closer to the bottom - something along those lines.

Do thank Mr Froude for all his hard work though :-)

[daiquiri]

Hmmm - interesting. I am not much of a swimmer, but it was definitely harder to swim at the 2 metre end than the 10 metre end.

2 meters? Well... :D

Actually, the shalow water effect depends on depth-to-draft ratio (h/T) too.
When (h/T) < 4 , the effect begins to be measurable.

For a 2-meter pool depth, it means that you might feel the effect if your draft is bigger than 2/4=0.5 meters.
Which again is related to the shape of your body.

The solution? A lots of excersize and a rigid diet will surely help. :D

[ancient kayaker]

Interesting phenom. I recall reading an article on planetary exploration a very long time ago which among other things predicted that fluids on planets with low gravity would have longer waves than on Earth.

For a given wave length, wave speed is proportional to the square root of Gee. On a low gravity planet (assuming liquid water could exist) that would reduce the hull speed of a boat. The fresh water on top of the more dense seawater would increase the length of a wave and reduce its speed, so presumably it has the same effect on hull speed. I believe the old "oil on troubled water" saying has the same roots.

Sea water is about 1.025 x density of freshwater, I'm not sure how that would affect wave length and speed in the dead water situation, but I'm guessing that the difference of 1/40 would reduce the apparent acceleration due to gravity at the interface by a factor of 40. That should, theoretically, reduce hull speed to sqrt(1/40) or 1/6.3. Nansen reported a 75% loss of speed, not quite as bad as I am predicting, but his boat may not have been achieving hull speed initially.

All this is way outside my area of expertise but it may suffice to persuade one of our hydrological experts to shoot me down in glorious flames.

[Tcubed]

Waves on planets with lower gravitational force than the earth would not produce shorter or longer waves. It will just alter the relation between wave length and wave speed. Less gravity would mean the same length wave goes slower.

The phase speed, c , of deep water surface gravity waves, is closely described by;

c = sqrt(gL/2pi)

where L is the wavelength, and g is acceleration due to gravity.
It is important to note that the effect of the air is ignored in this equation.
I unfortunately cannot remember the full equation offhand and i don't have my textbooks with me right now. Sea surface gravity waves are actually internal waves, i.e. waves travelling along a fluid interface. Because air is so much less dense than the water. the air is ignored to make things simpler with minimal loss of accuracy. I'll therefore carry on calling these 'surface waves' as is the custom. In waves travelling at the interface between two more similar fluids such as fresh water on salt water, the full equation must be used.

The effect of this is that these waves will travel much slower than 'surface waves', and can also have much greater amplitude/length ratios.

So the boat in "dead water" is trying to exceed its hull speed in that underwater fluid interface by a large factor and this creates a great deal of resistance. That's slightly oversimplyfying it but it's what's going on in a nutshell.

A sailboat on a salt water ocean on Mars would have a hull speed of;

Vh = sqrt(3.69L/2pi) so Vh mars would be 0.61 of Vh on earth.

Furthermore power to carry sail would be 0.376 of power to carry sail on earth. And boats would not float any higher or lower than on earth, by the way. So same viscous resistance, lower hull speeds and less sail, get ready for some slow martian sailing!!

[kach22i]

Interesting, I wonder if this is part of the reason the military in Norway uses Surface Effect Ships.

[marshmat]

Interesting, I wonder if this is part of the reason the military in Norway uses Surface Effect Ships.
That, and also they just enjoy beating the pants off anyone else's warships they happen to meet during international training exercises ;)