Quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube

The quasi-cyclic evolution of turbulence driven by a steady force in a periodic cube is investigated by means of large-eddy simulations with vanishing kinematic viscosity. By constraining the domain size so that only a single series of energy cascade events can take place, quasi-cyclic motions of multi-scale coherent vortices with a period of about 20T are realized. (Here, T denotes the turnover time of the largest eddies.) The observed cycle is composed of four periods characterized by activities of the largest- and smallest-resolvable-scale eddies. Vigorous energy cascade events, which last for about 2T, are observed between the two moments when large- and small-scale eddies are active. Even though we have examined only a special case of steady forces, such cyclic behavior of turbulence is likely to capture the essential dynamics of the regeneration cycle of multi-scale coherent structures, that is, the energy cascade in homogeneous isotropic turbulence at high Reynolds numbers.