ON THE LUNDGREN-TOWNSEND MODEL OF TURBULENT FINE SCALES

The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p+1 = (partial derivative u/partial derivative x)2p+1/[(partial derivative u/partial derivative x)2](2p+1)/2 to the hyperflatness F2p = (partial derivative u/partial derivative x)2p/[(partial derivative u/partial derivative x)2]p, p = 2,3,..., is constant independent of Taylor-Reynolds number R(lambda), as is the ratio of the 2pth moment of one component of the vorticity OMEGA2p = omega(x)2p/(omega(x)2)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortex-sheet-induced divergences in the integrals corresponding to omega(x)2p, p = 2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives OMEGA2p = OMEGA2pR(lambda)p/2-3/4, F2p = F2pR(lambda)p/2-3/4 and S2p+1 = S2p+1R(lambda)p/2-3/4, p = 2,3,..., with explicit calculation of the numbers OMEGA2p, F2p, and S2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)].