try this:
http://en.wikipedia.org/wiki/Ricci_flow
john
Turbulence of the gasses created in the combustion chamber as a result of only the shape of the head is somewhat intuitive. If we are only considering effects from the head shape, the motion of the gases (vectors) present during the combustion process is symmetrical as intuition would suggest. What really happens in the combustion chamber is more complex than the Maximum Squish Velocity (MSV) calculations that has many of the new engine builders debating. There seems to considerable debate in this new group over what the optimum calculated MSV number should be. Even if the MSV number was realistic it would be different for different types of engines and applications. The first time I read about MSV was around 1973 just after the release of an SAE paper that engineers from the McCullough engine plant in Lake Havasu Arizona authored. Since that time the subject of MSV has been rediscovered, debated, tested and then forgotten a few times. About every 10 to 15 years this cycle is repeated.
The vectors in the combustion chamber just before and during the combustion process is a result of more than what the effects of the squish band and the shape of the combustion chamber can contribute. There is considerable motion of the mixture in the cylinder as the piston approaches TDC. The motion of the gases are from the scavenging process and from the fresh mixture being pushed back into the cylinder by the exhaust pipe before exhaust port closing. Some of this motion is damped as the piston approaches top dead center. As the piston approaches TDC all of the vectors from the various sources are added together to form the resulting vectors present during the combustion process. The resulting vectors are not symmetrical and all vectors are not moving toward the spark plug as intuition would suggest.
I briefly skimmed over the text and the governing equations from the link on Ricci Flow. I did not see where it would be much use because of all of the unknown variables that are required for the calculations to be helpful in this situation. Maybe I missed something in the article that should have been obvious.