Fig. 6. A comparison of 2-D linear translation vs 3-D flapping translation. (A) 2-D linear translation. As an airfoil begins motion from rest, it generates a leading and trailing edge vortex. During translation, the trailing edge vortex is shed, leading to the growth of the leading edge vortex, which also sheds as the airfoil continues to translate. This motion leads to an alternate vortex shedding pattern from the leading and trailing edges, called the von Karman vortex street. This leads to a time dependence of the net aerodynamic forces (blue arrows) measured on the airfoil. (B) 3-D flapping translation. As in A, when an airfoil undergoing flapping translation starts from rest, it generates a leading and trailing edge vortex. However, as the motion progresses, the leading edge vortex attains a constant size and does not grow any further. Because no new vorticity is generated at the leading edge, there is no additional vorticity generated at the trailing edge and the airfoil obeys the Kutta condition. When established, the Kutta condition ensures that there is a net change in the direction of momentum resulting in a reactive aerodynamic force on the airfoil (black arrows; mv_i signifies initial momentum, mv_f signifies final momentum and mv signifies the difference between initial and final momenta). After establishment of the Kutta condition, the measured net aerodynamic forces (blue arrows) stay stable over a substantial period during translation and do not show time dependence. For Reynolds numbers of 100, this force acts normally to the wing and can be decomposed into mutually orthogonal lift and drag components (green arrows). Ultimately, however, the net downward momentum imparted by the airfoil to the fluid causes a downwash that slightly lowers the constant value of the net aerodynamic force on a steadily revolving wing.

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