High-order inertial range scaling exponents in incompressible turbulence using generalized extended self-similarity

Inertial range (IR) scaling exponents of velocity structure functions for incompressible turbulent flows can be measured very reliably at high-Reynolds numbers (Re). Extended self-similarity (ESS) has also allowed for measurement of these exponents at lower-Re. However, the measurements are limited to a range of orders where multiple theories provide similar predictions. Direct numerical simulations (DNS) of higher-Re flows for very long times, to guarantee statistical reliability, is computationally prohibitive on current generation of computers. Recent theoretical advances have however shown that scaling in certain turbulent quantities emerges in very low-Re flows, at least an order magnitude lower than needed for observing IR scaling. DNS in this regime, even with fine small-scale resolution, is currently feasible. In this talk, we measure the IR scaling exponents using generalized extended self-similarity at orders larger than reported in literature using highly resolved DNS at low to moderate-Re numbers. The particular focus is to improve reliability of IR scaling exponents in low-Re flows and determine the Re range where IR scaling is first observed. Measured scaling exponents are compared to different theories in order to enable discrimination between them.