# Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence

@article{Fang2015ShorttimeEO, title={Short-time evolution of Lagrangian velocity gradient correlations in isotropic turbulence}, author={L. Fang and Wouter J. T. Bos and G. D. Jin}, journal={Physics of Fluids}, year={2015}, volume={27}, pages={125102} }

We show by direct numerical simulation (DNS) that the Lagrangian cross correlation of velocity gradients in homogeneous isotropic turbulence increases at short times, whereas its auto-correlation decreases. Kinematic considerations allow to show that two invariants of the turbulent velocity field determine the short-time velocity gradient correlations. In order to get a more intuitive understanding of the dynamics for longer times, heuristic models are proposed involving the combined action of…

## 19 Citations

### Relation of the fourth-order statistical invariants of velocity gradient tensor in isotropic turbulence.

- PhysicsPhysical review. E
- 2016

We show by direct numerical simulations (DNSs) that in different types of isotropic turbulence, the fourth-order statistical invariants have approximately a linear relation, which can be represented…

### Theories and applications of second-order correlation of longitudinal velocity increments at three points in isotropic turbulence

- PhysicsPhysics Letters A
- 2018

### Quantitative description of non-equilibrium turbulent phenomena in compressors

- Physics, Engineering
- 2017

### Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

- Physics
- 2020

### Non-equilibrium turbulent phenomena in the flow over a backward-facing ramp

- PhysicsApplied Mathematics and Mechanics
- 2019

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid…

### Non-equilibrium turbulent phenomena in the flow over a backward-facing ramp

- PhysicsApplied Mathematics and Mechanics
- 2019

Non-equilibrium turbulence phenomena have raised great interests in recent years. Significant efforts have been devoted to non-equilibrium turbulence properties in canonical flows, e.g., grid…

### Velocity derivative skewness and its budget in non-equilibrium time-reversed turbulence

- PhysicsAIP Advances
- 2019

The velocity derivative skewness and its budget equation are analysed in non-equilibrium time-reversed turbulence. We show that the positive skewness is related to the behaviors of backward energy…

### Background scalar-level anisotropy caused by low-wave-number truncation in turbulent flows.

- PhysicsPhysical review. E
- 2017

It is rigorously shown that the truncation at low wave numbers always leads to background scalar-level anisotropy at large scales, and a simplified analytical model is introduced to explain the single-mode effects.

### Inter-scale transfer of the large-scale background anisotropy under periodic conditions

- PhysicsAIP Advances
- 2018

In numerical simulations of three-dimensional isotropy turbulence, low-wave-number truncation leads to large-scale anisotropy, but little anisotropy is generated at small scales. As the generally…

## 36 References

### Lagrangian time correlations of vorticity alignments in isotropic turbulence: observations and model predictions

- Physics, Environmental Science
- 2011

Motivated by results from recent particle tracking experiments in turbulence Xu et al. [Nature Phys. 7, 709 (2011)], we study the Lagrangian time correlations of vorticity alignments with the three…

### Elliptic model for space-time correlations in turbulent shear flows.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

An elliptic model for space-time correlations in turbulent shear flows is proposed based on a second order approximation to the iso-correlation contours, while Taylor's hypothesis implies a…

### Lagrangian refined Kolmogorov similarity hypothesis for gradient time evolution and correlation in turbulent flows.

- Environmental SciencePhysical review letters
- 2010

It is confirmed that when averaging over the entire domain, correlation functions decay on time scales on the order of the global Kolmogorov turnover time scale, but when performing the analysis in different subregions of the flow, turbulence intermittency leads to large spatial variability in the decay time scales.

### Velocity-Gradient Dynamics in Turbulence: Effect of Viscosity and Forcing

- Geology
- 2003

The restricted Euler equation is a promising but incomplete model for velocity-gradient dynamics in turbulent flows. While it captures many of the geometric features of the vorticity vector and the…

### Orientation statistics of small particles in turbulence

- Physics
- 2011

The statistics of the alignment of axisymmetric microscopic particles in fully developed turbulent flow is studied numerically and theoretically. Direct numerical simulations (DNS) of turbulent flows…

### Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

A scale-similarity model for Lagrangian two-point, two-time velocity correlations (LVCs) in isotropic turbulence is developed from the Kolmogorov similarity hypothesis: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

### Lagrangian dynamics and statistical geometric structure of turbulence.

- PhysicsPhysical review letters
- 2006

A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends.

### Space-time correlations of fluctuating velocities in turbulent shear flows.

- Geology, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This model predicts a universal form of the space-time correlations with the two characteristic velocities: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

### Lagrangian Dynamics and Models of the Velocity Gradient Tensor in Turbulent Flows

- Computer Science
- 2011

Various models that aim at understanding small-scale motions in turbulence using a small number of ordinary differential equations, written either as a low-dimensional dynamical system or as a set of stochastic differential equations are reviewed.

### Effects of subgrid-scale modeling on Lagrangian statistics in large-eddy simulation

- Physics, Environmental Science
- 2008

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no…