Influence of the spatial resolution on fine-scale features in DNS of turbulence generated by a single square grid

We focus in this paper on the effect of the resolution of direct numerical simulations (DNS) on the spatio-temporal development of the turbulence downstream of a single square grid. The aims of this study are to validate our numerical approach by comparing experimental and numerical one-point statistics downstream of a single square grid and then investigate how the resolution is impacting the dynamics of the flow. In particular, using the Q–R diagram, we focus on the interaction between the strain-rate and rotation tensors, the symmetric and skew-symmetric parts of the velocity gradient tensor, respectively. We first show good agreement between our simulations and hot-wire experiment for one-point statistics on the centreline of the single square grid. Then, by analysing the shape of the Q–R diagram for various streamwise locations, we evaluate the ability of under-resolved DNS to capture the main features of the turbulence downstream of the single square grid.

[1]  J. Christos Vassilicos,et al.  Dissipation in Turbulent Flows , 2015 .

[2]  Javier Jiménez,et al.  Cascades in Wall-Bounded Turbulence , 2012 .

[3]  Jose C. F. Pereira,et al.  Erratum: “Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets” [Phys. Fluids 20, 055101 (2008)] , 2009 .

[4]  William H. Press,et al.  Numerical recipes , 1990 .

[5]  Christos Vassilicos,et al.  Turbulence without Richardson-Kolmogorov Cascade , 2009, 0911.0841.

[6]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[7]  Jason Monty,et al.  Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation , 2009, Journal of Fluid Mechanics.

[8]  Christos Vassilicos,et al.  The decay of turbulence generated by a class of multiscale grids , 2011, Journal of Fluid Mechanics.

[9]  P. Vieillefosse,et al.  Internal motion of a small element of fluid in an inviscid flow , 1984 .

[10]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[11]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[12]  G. S. Martin.  Dissipation , 1904, The American journal of dental science.

[13]  R. Moser,et al.  One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to δ+ ≈ 2000 , 2013 .

[14]  Keiko Takahashi,et al.  Large-scale forcing with less communication in finite-difference simulations of stationary isotropic turbulence , 2011, J. Comput. Phys..

[15]  J. C. Vassilicos,et al.  Axisymmetric turbulent wakes with new nonequilibrium similarity scalings. , 2013, Physical review letters.

[16]  Victor Yakhot,et al.  Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations , 2005, nlin/0506038.

[17]  M. S. Chong,et al.  A general classification of three-dimensional flow fields , 1990 .

[18]  Arkady Tsinober,et al.  An informal conceptual introduction to turbulence , 2009 .

[19]  Y. Kaneda,et al.  Study of High-Reynolds Number Isotropic Turbulence by Direct Numerical Simulation , 2009 .

[20]  F. Bisetti,et al.  Statistics and scaling of turbulence in a spatially developing mixing layer at Reλ = 250 , 2012 .

[21]  A. Kolmogorov,et al.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[22]  E. M. Lifshitz,et al.  Course in Theoretical Physics , 2013 .

[23]  J. C. Vassilicos,et al.  Interscale energy transfer in decaying turbulence and vorticity–strain-rate dynamics in grid-generated turbulence , 2013 .

[24]  Chia-chiao Lin,et al.  On the Development of Turbulence , 1944 .

[25]  Bharathram Ganapathisubramani,et al.  Particle image velocimetry study of fractal-generated turbulence , 2012, Journal of Fluid Mechanics.

[26]  Sylvain Laizet,et al.  High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy , 2009, J. Comput. Phys..

[27]  J. Vassilicos,et al.  Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient , 2014, Journal of Fluid Mechanics.

[28]  Development of turbulence behind the single square grid , 2014 .

[29]  Ning Li,et al.  Incompact3d: A powerful tool to tackle turbulence problems with up to O(105) computational cores , 2011 .

[30]  A. Kolmogorov.  Dissipation of energy in the locally isotropic turbulence , 1941, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[31]  Jose C. F. Pereira,et al.  Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets , 2008 .

[32]  A. N. Kolmogorov.  Equations of turbulent motion in an incompressible fluid , 1941 .

[33]  P. Schlatter,et al.  Simulation and validation of a spatially evolving turbulent boundary layer up to Reθ = 8300 , 2014 .

[34]  P. Vieillefosse,et al.  Local interaction between vorticity and shear in a perfect incompressible fluid , 1982 .

[35]  Sylvain Laizet,et al.  Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation , 2011, J. Comput. Phys..

[36]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .

[37]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[38]  S. Laizet,et al.  The effects of resolution and noise on kinematic features of fine-scale turbulence , 2011 .

[39]  Diego Donzis,et al.  Dissipation and enstrophy in isotropic turbulence: Resolution effects and scaling in direct numerical simulations , 2008 .

[40]  Diego Donzis,et al.  Dissipation, enstrophy and pressure statistics in turbulence simulations at high Reynolds numbers , 2012, Journal of Fluid Mechanics.

[41]  J. C. Vassilicos,et al.  Universal dissipation scaling for nonequilibrium turbulence. , 2011, Physical review letters.

[42]  Brian J. Cantwell,et al.  Exact solution of a restricted Euler equation for the velocity gradient tensor , 1992 .

[43]  J. C. Vassilicos,et al.  Energy dissipation and flux laws for unsteady turbulence , 2015 .

[44]  Dan S. Henningson,et al.  Turbulent boundary layers up to Reθ=2500 studied through simulation and experiment , 2009 .

[45]  Jerry Westerweel,et al.  Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment , 1994, Journal of Fluid Mechanics.