source: http://library.thinkquest.org/11902/physics/curve2.html
source: http://library.thinkquest.org/11902/physics/curve2.html
So above is an image of a baseball that is encountering a flow from the left as it rotates. Typical Reynolds numbers for a pitched baseball are 1.5 x 10E5, which is very close to the critical Reynolds number. From the previous examples of boundary seperation, we know that below this critical value, there is a laminar seperation that is farther upstream, while above the critical value, there is a turbulent seperation farther downstream.
They key to the curveball is the rotation. Remembering our no-slip boundary conditions, we realize that the fluid velocity on the upper surface of the ball will be in the opposite direction of the bulk flow. Similarly, on the bottom of the ball the fluid velocity will be in the same direction as the bulk flow. This has the effect of increasing the Reynolds number at the top, while decreasing it at the bottom. Since the Reynolds number is close to the critical Reynolds number, the increase at the top can be enough to produce the transition to turbulent seperation, and move the point of seperation farther downstream (to the right). Meanwhile, the bottom of the ball still has a laminar seperation that is farther upstream. This results in a wake that spreads out more quickly downwards that upwards. This non-symmetric wake results in a larger pressure on the bottom of the ball than at the top of the ball. The difference in pressures gives rise to a force, known as the Magnus Force, which causes the ball to move upwards.
Bibliography
Back to boundary seperation
Back to Stokes Flow