Direct numerical simulation of spiral turbulence

In this paper, we present results of three-dimensional direct numerical simulations of the spiral turbulence phenomenon in a range of moderate Reynolds numbers, in which alternating intertwined helical bands of turbulent and laminar fluids coexist and propagate between two counter-rotating concentric cylinders. We show that the turbulent spiral is comprised of numerous small-scale azimuthally elongated vortices, which align into and collectively form the barber-pole-like pattern. The domain occupied by such vortices in a plane normal to the cylinder axis resembles a 'crescent moon', a shape made well known by Van Atta with his experiments in the 1960s. The time-averaged mean velocity of spiral turbulence is characterized in the radial axial plane by two layers of axial flows of opposite directions. We also observe that, as the Reynolds number increases, the transition from spiral turbulence to featureless turbulence does not occur simultaneously in the whole domain, but progresses in succession from the inner cylinder towards the outer cylinder. Certain aspects pertaining to the dynamics and statistics of spiral turbulence and issues pertaining to the simulation are discussed.