Role of Fourier phase dynamics in decaying turbulence

A previous study in stochastically forced 1D Burgers flows reveals a dynamical synchronization of Fourier triadic phases during burst events associated with intense forward energy fluxes (Murray and Bustamante, J. Fluid Mech. 850, 624 (2018)0022-112010.1017/jfm.2018.454. Conversely, it is yet to be determined whether the dynamical evolution of Fourier phases is necessary for forming forward energy cascades in more general flow systems, particularly in 3D turbulent flows. We propose a "frozen-phase"experiment in which only the Fourier amplitudes evolve temporally, with a fixed set of Fourier phases prescribed. The method employed to freeze the phases can be considered a designed forcing term in the spectral space that only acts on the evolution equation of Fourier phases. The results suggest the essential role of Fourier phase dynamics in the formation of a "standard"energy cascade in 3D turbulent flows. However, forming an "attenuated"energy cascade without any phase dynamics is still possible. These findings are supported by the values of longitudinal velocity gradient skewness and the Kolmogorov constants, which deviate from classical ones when the phases are frozen.