Analytical Services

Fluid Flow Analysis

Why is “sh” so much louder than “s”, “f”, or “th”?

Scientists had suspected that high-pressure air hitting the back of the teeth might be responsible. 

In 2004, we used the technique of conformal mapping to produce a full mathematical model of the air flow. Conformal mapping allows us to convert (or “map”) a problem with complicated geometry to another that has simpler geometry but very similar equations. Then we solve the equations for that simpler geometry and finally reverse the mapping. The result is a solution for the original problem.

It turned out that not only did a jet of air need to hit the back of the teeth, it also needed to be guided down in the narrow channel between the upper and lower teeth.  Otherwise: no loud sound!