# The effects of resolution and noise on kinematic features of fine-scale turbulence

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## Abstract

The effect of spatial resolution and experimental noise on the kinematic fine-scale features in shear flow turbulence is investigated by means of comparing numerical and experimental data. A direct numerical simulation (DNS) of a nominally two-dimensional planar mixing layer is mean filtered onto a uniform Cartesian grid at four different, progressively coarser, spatial resolutions. Spatial gradients are then calculated using a simple second-order scheme that is commonly used in experimental studies in order to make direct comparisons between the numerical and previously obtained experimental data. As expected, consistent with other studies, it is found that reduction of spatial resolution greatly reduces the frequency of high magnitude velocity gradients and thereby reduces the intermittency of the scalar analogues to strain (dissipation) and rotation (enstrophy). There is also an increase in the distances over which dissipation and enstrophy are spatially coherent in physical space as the resolution is coarsened, although these distances remain a constant number of grid points, suggesting that the data follow the applied filter. This reduction of intermittency is also observed in the eigenvalues of the strain-rate tensor as spatial resolution is reduced. The quantity with which these eigenvalues is normalised is shown to be extremely important as fine-scale quantities, such as the Kolmogorov length scale, are showed to change with different spatial resolution. This leads to a slight change in the modal values for these eigenvalues when normalised by the local Kolmogorov scale, which is not observed when they are normalised by large-scale, resolution-independent quantities. The interaction between strain and rotation is examined by means of the joint probability density function (*pdf*) between the second and third invariants of the characteristic equation of the velocity gradient tensor, *Q* and *R* respectively and by the alignments between the eigenvectors of the strain-rate tensor and the vorticity vector. Gaussian noise is shown to increase the divergence error of a dataset and subsequently affect both the *Q*–*R* joint *pdf* and the magnitude of the alignment cosines. The experimental datasets are showed to behave qualitatively similarly to the numerical datasets to which Gaussian noise has been added, confirming the importance of understanding the limitations of coarsely resolved, noisy experimental data.

## Keywords

Particle Image Velocimetry Direct Numerical Simulation Joint Probability Density Function Direct Numerical Simulation Data Velocity Gradient Tensor## Notes

### Acknowledgments

The authors would like to thank EPSRC for providing the computing resources on HECToR through the Resource Allocation Panel and for funding the experimental research through Grant No. EP/F056206. Funding from the Royal Aeronautical Society for ORHB is also greatly appreciated.

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