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

The effects of resolution and noise on kinematic features of fine-scale turbulence
The effects of resolution and noise on kinematic features of fine-scale turbulence
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.
0723-4864
1417-1437
Buxton, O.R.H.
02f9e46b-0466-4294-9640-62dc7c1a1766
Laizet, S.
74f95ec1-e915-427c-a1a3-d13e8729d0fb
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052
Buxton, O.R.H.
02f9e46b-0466-4294-9640-62dc7c1a1766
Laizet, S.
74f95ec1-e915-427c-a1a3-d13e8729d0fb
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052

Buxton, O.R.H., Laizet, S. and Ganapathisubramani, B. (2011) The effects of resolution and noise on kinematic features of fine-scale turbulence. Experiments in Fluids, 51 (5), 1417-1437. (doi:10.1007/s00348-011-1159-2).

Record type: Article

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.

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More information

Published date: November 2011
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 354999
URI: https://eprints.soton.ac.uk/id/eprint/354999
ISSN: 0723-4864
PURE UUID: 813e63df-16f0-4b8b-bb1b-6c330173c404
ORCID for B. Ganapathisubramani: ORCID iD orcid.org/0000-0001-9817-0486

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Date deposited: 12 Aug 2013 11:15
Last modified: 06 Jun 2018 12:33

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