Sign-singular measure and its association with turbulent scalings

Turbulent quantities such as vorticity, which oscillate in sign on very fine scales, have recently been characterized by sign-singular measures [E. Ott, Y. Du, K. R. Sreenivasan, A. Juneja, and A. K. Suri, Phys. Rev. Lett. 69, 2654 (1992)] and quantified by the so-called cancellation exponent. Here, the connection between the cancellation exponent and other known exponents for velocity structure functions and multifractal spectrum of the energy dissipation field is discussed. Comparison with high-Reynolds-number experimental data in one dimension and direct measurements of vorticity in a plane in moderate-Reynolds-number flows reveals excellent internal consistency. Estimates for second-order cancellation exponent are presented.