Energy transfer and intermittency in four-dimensional turbulence

Abstract

The energy transfer and small scale intermittency in decaying turbulence in four dimensions are studied by direct numerical simulation and by spectral theory. It is found that (1) a 1∕2 law, −(1∕2)ε¯r, in four dimensional (4D) for the longitudinal third-order structure function holds, (2) the energy transfer in 4D is more efficient than in three dimensional (3D), (3) the Kolmogorov constant in 4D is K4=1.28 which is smaller than K3=1.72 in 3D, (4) the velocity gradient intermittency is stronger than in 3D, while (5) the total-energy dissipation rate in 4D is less intermittent than in 3D. The conflicting trends in (4) and (5) are explained by the changes in the balance between the convective and pressure terms as the dimension increases.