Pouring oil on choppy water to calm it , does it work and if so how? Near where I live, local fishermen often bring cans of castor oil with them, to calm the water around their boats, if they feel bad weather is due. 
They claim this method of sea calming works, (possibly because it worked for their fathers, and their father's fathers.....).
Does  this idea have a factual basis, or is it a tall tale/superstition?  The physics department of my local university is currently conducting sea trials regarding the process, so they seem to take it seriously enough.
Have we any evidence that it does work, even as a possibly beneficial effect from serious adverse environmental events such as oil tanker leaks? 
Is there any theory regarding the mechanism involved?
EDIT Below  the answer from Floris,  Chris White wrote this comment, which I just had to steal:

An amazing quote from Ben Franklin via Tanford's Ben Franklin Stilled the Waves quoted in the first article, attesting to the efficacy of this method: "the oil, though not more than a teaspoonful, produced an instant calm over a space of several yards square, which spread amazingly, and extended itself gradually till it reached the lee side, making all that quarter of the pond, perhaps half an acre, as smooth as a looking glass." This from a teaspoon of presumed olive oil!

 A: Yes it works. But let's not use it on a massive scale, lest we damage the ecosystem (tip of the hat to @phi1123).
A hint to the mechanism can be found in Behroozi et al (Am J Phys, 2007)
They state in the abstract:

From the attenuation data at frequencies between 251 and 551Hz, we conclude that the calming effect of oil on surface waves is principally due to the dissipation of wave energy caused by the Gibbs surface elasticity of the monolayer, with only a secondary contribution from the reduction in surface tension. Our data also indicate that the surface-dilational viscosity of the oil monolayer is negligible and plays an insignificant role in calming the waves.

(my emphasis)
Dissipation of wave energy. The key to waves getting big is that a) wave energy is added by the motion of air over the surface, and b) the energy imparted is not immediately dissipated. In a sense, the oil acts as a "Q spoiler" - a little bit of energy dissipation in each cycle means that the wave just doesn't get a chance to build up. 
A similar thing is explained in the book "Waves on Fluids" by James Lighthill (Cambridge University Press, 2001).  On page 237 it states:

It is departures of the surface tension $T$ from its equilibrium value that can result in such surface dissipation. In a fluid such
  that small wave motions generate small variations in $T$, a net
  $X$-component of force $$(\partial T/\partial x) \delta x$$ must act
  on a strip of surface of width $\delta x$ with frontiers of unit length
  parallel to the $y$-axis, even though on linear theory the same small
  variations make no change to the $z$-component. In the surface
  boundary layer, therefore, the tangential stress changes from (80) not
  to zero but to the value $$p_{xx} = -\partial T/\partial x$$
Needed to balance the $x$-component ($\partial T/\partial x)$ of
  surface force per unit area.
There are conditions when in the surface boundary layer the tangential stresses increase in magnitude so enormously from the internal value (80) to the surface value (87) that the resulting surface dissipation (extra viscous dissipation due to enhanced shearing stresses within the surface boundary layer) greatly exceeds the rate of internal dissipation. This is the mechanism responsible for the proverbial calming effect of 'oil on troubled waters'.

In other words - the thin layer of oil causes a rapid change in tangential stresses near the surface, leading to energy dissipation. This prevents the buildup of wave energy - especially at the shorter wavelengths. This not only makes the water appear smoother ("smooth as a looking glass", in the Franklin quote) but in the process reduces the "grip" of the wind on the water - making energy transfer from wind to water more difficult.
A: Before everyone freaks out, no, you don't use petroleum oil. You use vegetable, fish or animal oil. In earlier times, whale oil would be used. The OP's picture looks like a fuel oil leak, not an attempt at wave calming.
I have seen references of this technique being used since at least the early 1800s, probably much earlier.  Ernest Shackleton made use of it in 1916 during the Voyage Of The James Caird across 800 miles of Arctic Ocean to calm the very rough seas.
"The Popular Science Monthly, Volume 43", from May 1893, contains an article "Why A Film Of Oil Can Calm The Sea" by G. W. Littlehales from the US Hydrographic Office (page 494).  Here's a description of one schooner captain's apparatus and its effectiveness in heavy storm.

The sails were blown away, men washed from the pumps, and the boats and other things above the deck wrecked by the heavy seas... Two wooden, ten-gallon kegs, containing boiled linseed [flax] oil, were lashed to the quarters of the vessel. The oil was allowed to ooze out through two small holes in the heads of the kegs. The effect was all that could be desired. After the oil had spread, no water came on board, the men returned to the pumps, the vessel was pumped out, and the decks were cleaned up. During the sixteen hours in which the oil was used eight gallons were expended.

From that testimony, and the article mentions examining thousands of reports, it seems very effective and economical.  Just two quarts per hour of thick, heavy oil...

...when allowed to drop into the sea soon spreads over its surface, forming an oily layer within the area of which the waves, instead of breaking, become huge rollers upon which the vessels rise and fall without shocks and without shipping any water.

The oil doesn't prevent the waves, but it prevents them from breaking and spraying water onto the deck and into the ship.
The article goes on in some detail describing wave action.  What it comes down to is the oil acts as a lubricant between the wind and the water.  It smooths the surface of the water so the wind has no rough surface to drag on and cause the waves to spray and break.

When wind blows over water, all the air does not pass over the surface of the water. On account of the high degree of adhesion between air and water, a thin stratum of air remains in contact with the water, and it is the action of the internal friction or viscosity of air tending to draw this stratum along which causes the tractive effect of wind on water.
When a film of oil is spread over the surface, this tractive force is not brought to bear on the surface of the water as long as the film remains unbroken... The surface of the water is thus shielded from the action of the wind... the only action of the wind in such a case is to move the film over the surface of the water.

