Universal scaling laws of boundary-driven turbulence

Abstract: Turbulence is a fundamental flow phenomenon, typically anisotropic at large scales and approximately isotropic at small scales. The classical Kolmogorov scaling laws (2/3, -5/3 and 4/5) have been well-established for turbulence without small-scale body forcing, describing second-order velocity structure functions, energy spectra, and third-order velocity structure functions in an intermediate small-scale range. However, their validity boundary remains unclear. Here, we identify new 1 and -2 scaling laws (replacing 2/3 and -5/3 laws) alongside the unchanged 4/5 law in the core region of boundary-driven turbulence, where energy is injected solely through viscous friction at moving boundaries. Local isotropy is recovered after high-pass filtering. Notably, odd-order velocity structure functions with and without absolute value exhibit distinct scaling exponents. A characteristic speed in the inertial range, derived from the constant ratio of third- to second-order structure functions, quantifies the time-averaged projectile speed at the bulk interface. Based on energy dissipation rate and the characteristic speed, a phenomenological framework for structure functions is developed together with a model for probability distributions of velocity increment at distinct small-scales. The universal scaling laws formulated can produce the full set of scaling exponents for low- and high-order velocity structure functions, including both the odd-orders' with and without absolute value, which are validated by direct numerical simulations and experimental datasets.