Existence of positive skewness of velocity gradient in early transition

The present study uses direct numerical simulations to calculate two different transitional flows from laminar flow to turbulence, that is, the two-scale wake flow and the two-dimensional Reyleigh-Taylor unstable flow, respectively. Both results show that the skewness of the longitudinal velocity gradient, , can become positive in the early transition stage, which is beyond our expectation since the turbulent equilibrium state always implies negative values of . These phenomena are explained analytically by considering only two dominant Fourier modes with harmonic relations. It is illustrated that the sign of is not only affected by the amplitudes of the perturbation velocities, but also related to their phases. We expect that the present results will be helpful for understanding the formation of turbulent equilibrium state and for constructing a new measurable criterion of the transition onset.