Statistical Research Of Turbulent Velocity Gradient In Three-dimensional Turbulent Flows

Most flows in nature and practical engineering application are turbulence. The energy dissipation prevents an unlimited growth of turbulence, playing an important role in all kinds of flows. The turbulent energy dissipation rate determines many industrial processes for the production of quality and work efficiency. The mechanism of turbulent dissipation rate is one of the most basic turbulent topics.In this paper, the energy dissipation, the pseudo-dissipation, and the traditional surrogate dissipation along the Lagrangian tracer particle is considered in three-dimensional homogeneous and isotropic turbulent flows with Reλ= 400 in a 2048 cubic. Lagrangian turbulent cascade is also investigated under the same database at the same time. The results as follows:(1) It is found that intermittent characteristics of full energy dissipation and multifractal theory are in a good agreement. However, the contribution of each component of the full energy dissipation does not satisfy the classical theory prediction. Furthermore, the cross correlation between the traditional surrogate dissipation and pseudo-dissipation, and the full energy dissipation rate is about 0.6, indicating a medial correlation. Therefore, the intermittent parameter provided by the traditional surrogate dissipation is then biased, showing a more intermittent.(2) Both the energy dissipation rate ε and the local time-averaged εT agree rather well with the lognormal distribution hypothesis. Several statistics are then examined. It is found that the autocorrelation function ρ(τ) of ln(ε(t))and variance σ2(τ)of ln(ετ(t)) obey a log-law with scaling exponent β=0.30 compatible with the intermittent parameter μ= 0.30.(3) The qth-order moment of ετ has a clear power law on the inertial range. The measured scaling exponent KL(q) agrees remarkably withq-ζL(2q) where ζL(2q) is the scaling exponent estimated using the Hilbert methodology. All of these results suggest that the dissipation along Lagrangian trajectories could be modelled by a multiplicative cascade.