Discovery of the zeroth law of helicity spectrum in the pre-inertial range of wall turbulence

Abstract

We report an unprecedented existence of the zeroth law of helicity spectrum (i.e., the helicity spectrum becomes independent of the wavenumber) in the transition from production range to inertial range, herein termed the pre-inertial range, of wall turbulence. The zeroth law is explained by the superposition effect of the forward joint cascade of energy and helicity caused by twisting and stretching of wall-attached superstructures in an equilibrium layer. The phenomenological model perfectly predicts the zeroth law in the pre-inertial range. Experimental data support the existence of the zeroth law.