Calculation of velocity structure functions for vortex models of isotropic turbulence

Velocity structure functions (up 82up) m are calculated for vortex models of isotropic turbulence. An integral operator is introduced which defines an isotropic two-point field from a volume-orientation average for a specific solution of the Navier–Stokes equations. Applying this to positive integer powers of the longitudinal velocity difference then gives explicit formulas for (up 82up) m as a function of order m and of the scalar separation r . Special forms of the operator are then obtained for rectilinear stretched vortex models of the Townsend–Lundgren type. Numerical results are given for the Burgers vortex and also for a realization of the Lundgren-strained spiral vortex, and comparison with experimental measurement is made. In an Appendix, we calculate values of the velocity-derivative moments for the Townsend–Burgers model. © 1996 American Institute of Physics. @S1070-6631~96!00611-3#