# Statistical properties of the velocity field for the 3D hydrodynamic turbulence onset

## TL;DR

This paper investigates the statistical properties of velocity fields during the onset of 3D hydrodynamic turbulence, revealing power-law scaling, intermittency, and anisotropic effects through extensive numerical simulations.

## Contribution

It provides new insights into the scaling behavior and intermittency of velocity structure functions during turbulence onset, highlighting similarities with stationary turbulence.

## Key findings

- Power-law scaling in velocity structure functions during turbulence onset
- Intermittency and anomalous scaling of velocity moments
- Longitudinal third-order moments follow Kolmogorov's 4/5-law despite anisotropy

## Abstract

We study the statistical correlation functions for the three-dimensional hydrodynamic turbulence onset when the dynamics is dominated by the pancake-like high-vorticity structures. With extensive numerical simulations, we systematically examine the two-points structure functions (moments) of velocity. We observe formation of the power-law scaling for both the longitudinal and the transversal moments in the same interval of scales as for the energy spectrum. The scaling exponents for the velocity structure functions demonstrate the same key properties as for the stationary turbulence case. In particular, the exponents depend on the order of the moment non-trivially, indicating the intermittency and the anomalous scaling, and the longitudinal exponents turn out to be slightly larger than the transversal ones. When the energy spectrum has power-law scaling close to the Kolmogorov's one, the longitudinal third-order moment shows close to linear scaling with the distance, in line with the Kolmogorov's 4/5-law despite the strong anisotropy.