Structure of lift-generated rolled-up vortices

Widely used analytical models describing the structure of lift-generate d vortices behind aircraft wings (e.g., models of Betz or Lamb) are generally not in acceptable agreement with experiments. The lack in conservation of vortical dispersion and rotational energy, which is connected with the induced drag of the generating wing, is considered as a reason for this discrepancy. The model of Lamb is modified in a simple way to account for the conservation laws. These modifications yield a reduction in the core radius and a remarkable increase in the maximum tangential speed. A comparison with experiments is made and reasonable agreement is found. For the modification of the vorticity distribution in the Lamb model, the Kirchhoff-Routh function is used. This function is proportional to the rotational energy for a continuously spaced array of point vortices having the proper vorticity. The proposed model can be adapted to arbitrary vorticity distributions and, hence, wing loadings. a c CR De / k, p q r rK s t u vm W 7r, 7 5