Cascades, backscatter and conservation in numerical models of two‐dimensional turbulence
dc.contributor.author | Thuburn, John | en_US |
dc.contributor.author | Kent, James | en_US |
dc.contributor.author | Wood, Nigel | en_US |
dc.date.accessioned | 2014-05-21T18:02:33Z | |
dc.date.available | 2015-04-01T19:59:05Z | en_US |
dc.date.issued | 2014-01 | en_US |
dc.identifier.citation | Thuburn, John; Kent, James; Wood, Nigel (2014). "Cascades, backscatter and conservation in numerical models of two‐dimensional turbulence." Quarterly Journal of the Royal Meteorological Society 140(679): 626-638. | en_US |
dc.identifier.issn | 0035-9009 | en_US |
dc.identifier.issn | 1477-870X | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/106663 | |
dc.description.abstract | The equations governing atmospheric flow imply transfers of energy and potential enstrophy between scales. Accurate simulation of turbulent flow requires that numerical models, which have finite resolution and truncation errors, adequately capture these interscale transfers, particularly between resolved and unresolved scales. It is therefore important to understand how accurately these transfers are modelled in the presence of scale‐selective dissipation or other forms of subgrid model. Here, the energy and enstrophy cascades in numerical models of two‐dimensional turbulence are investigated using the barotropic vorticity equation. Energy and enstrophy transfers in spectral space due to truncated scales are calculated for a high‐resolution reference solution and for several explicit and implicit subgrid models at coarser resolution. The reference solution shows that enstrophy and energy are removed from scales very close to the truncation scale and energy is transferred (backscattered) into the large scales. Some subgrid models are able to capture the removal of enstrophy from small scales, though none are scale‐selective enough; however, none are able to capture accurately the energy backscatter. We propose a scheme that perturbs the vorticity field at each time step by the addition of a particular vorticity pattern derived by filtering the predicted vorticity field. Although originally conceived as a parametrization of energy backscatter, this scheme is best interpreted as an energy ‘fixer’ that attempts to repair the damage to the energy spectrum caused by numerical truncation error and an imperfect subgrid model. The proposed scheme improves the energy and enstrophy behaviour of the solution and, in most cases, slightly reduces the root mean square vorticity errors. | en_US |
dc.publisher | John Wiley & Sons, Ltd. | en_US |
dc.subject.other | Cascade | en_US |
dc.subject.other | Backscatter | en_US |
dc.title | Cascades, backscatter and conservation in numerical models of two‐dimensional turbulence | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Atmospheric, Oceanic and Space Sciences | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Atmospheric, Oceanic and Space Sciences, University of Michigan, Ann Arbor, MI, USA | en_US |
dc.contributor.affiliationother | College of Engineering, Mathematics and Physical Sciences, University of Exeter, UK | en_US |
dc.contributor.affiliationother | Met Office, FitzRoy Road, Exeter UK | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/106663/1/2166_ftp.pdf | |
dc.identifier.doi | 10.1002/qj.2166 | en_US |
dc.identifier.source | Quarterly Journal of the Royal Meteorological Society | en_US |
dc.identifier.citedreference | Rhines PB. 1979. Geostrophic turbulence. Annu. Rev. Fluid Mech. 11: 401 – 441. | en_US |
dc.identifier.citedreference | Koshyk JN, Boer GJ. 1994. Parameterization of dynamical subgrid‐scale processes in a spectral GCM. J. Atmos. Sci. 52: 965 – 976. | en_US |
dc.identifier.citedreference | Kraichnan RH. 1975. Statistical dynamics of two‐dimensional flow. J. Fluid Mech. 67: 155 – 175. | en_US |
dc.identifier.citedreference | Kraichnan RH. 1976. Eddy viscosity in 2 and 3 dimensions. J. Atmos. Sci. 33: 1521 – 1536. | en_US |
dc.identifier.citedreference | Leonard BP, MacVean MK, Lock AP. 1993. Positivity‐preserving numerical schemes for multidimensional advection. NASA Technical Memorandum 106055. | en_US |
dc.identifier.citedreference | Lin SJ. 2004. A ‘vertically Lagrangian’ finite‐volume dynamical core for global models. Mon. Weather Rev. 132: 2293 – 2307. | en_US |
dc.identifier.citedreference | Margolin LG, Rider WJ. 2002. A rationale for implicit turbulence modeling. Int. J. Numer. Meth. Fluids 39: 821 – 841. | en_US |
dc.identifier.citedreference | Margolin LG, Rider WJ. 2007. Numerical regularization: the numerical analysis of implicit subgrid models. In Implicit Large‐Eddy Simulation, Grinstein FF, Margolin LG, Rider WJ (eds). Cambridge University Press: Cambridge, UK; 195 – 221. | en_US |
dc.identifier.citedreference | Mason PJ, Thomson DJ. 1992. Stochastic backscatter in large‐eddy simulations of boundary layers. J. Fluid Mech. 242: 51 – 78. | en_US |
dc.identifier.citedreference | Neale RB, Chen C‐C, Gettelman A, Lauritzen PH, Park S, Williamson DL, Conley AJ, Garcia R, Kinnison D, Lamarque J‐F, Marsh D, Mills M, Smith AK, Tilmes S, Vitt F, Cameron‐Smith P, Collins WD, Iacono MJ, Rasch PJ, Taylor MA. 2010. Description of the NCAR Community Atmosphere Model (CAM 5.0). NCAR Technical Note NCAR/TN‐486 + STR. | en_US |
dc.identifier.citedreference | Pietarila Graham J, Ringler T. 2013. A framework for the evaluation of turbulence closures used in mesoscale ocean large‐eddy simulations. Ocean Model. (In press). | en_US |
dc.identifier.citedreference | Robert A. 1966. The integration of a low order spectral form of the primitive meteorological equations. J. Meteorol. Soc. Japan 44: 237 – 245. | en_US |
dc.identifier.citedreference | Sadourny R, Basdevant C. 1985. Parameterization of subgrid scale barotropic and baroclinic eddies in quasi‐geostrophic models: anticipated potential vorticity method. J. Atmos. Sci. 42: 1353 – 1363. | en_US |
dc.identifier.citedreference | Salmon R. 1998. Lectures on Geophysical Fluid Dynamics. Oxford University Press: Oxford. | en_US |
dc.identifier.citedreference | Shutts G. 2005. A kinetic energy backscatter algorithm for use in ensemble prediction systems. Q. J. R. Meteorol. Soc. 131: 3079 – 3102. | en_US |
dc.identifier.citedreference | Smagorinsky J. 1963. General circulation experiments with the primitive equations. I. The basic experiment. Mon. Weather. Rev. 91: 99 – 164. | en_US |
dc.identifier.citedreference | Thuburn J. 1996. Multidimensional flux‐limited advection schemes. J. Comput. Phys. 123: 74 – 83. | en_US |
dc.identifier.citedreference | Thuburn J. 2008. Some conservation issues for the dynamical cores of NWP and climate models. J. Comput. Phys. 227: 3715 – 3730. | en_US |
dc.identifier.citedreference | Williamson DL. 2007. The evolution of dynamical cores for global atmospheric models. J. Meteorol. Soc. Japan 85B: 241 – 269. | en_US |
dc.identifier.citedreference | Williamson DL, Olson JG, Jablonowski J. 2009. Two dynamical core formulation flaws exposed by a baroclinic instability test case. Mon. Weather Rev. 137: 790 – 796. | en_US |
dc.identifier.citedreference | WGNE. 2003. WMO Atmospheric Research and Environment Programme. Report No. 18, CAS/JSC Working Group on Numerical Experimentation. | en_US |
dc.identifier.citedreference | Arakawa A. 1966. Computational design for long‐term numerical integration of the equations of fluid motion: two‐dimensional incompressible flow. Part I. J. Comput. Phys. 1: 119 – 143. | en_US |
dc.identifier.citedreference | Asselin R. 1972. Frequency filter for time integrations. Mon. Weather Rev. 100: 487 – 490. | en_US |
dc.identifier.citedreference | Batchelor GK. 1969. Computation of the energy spectrum in homogeneous two‐dimensional turbulence. Phys. Fluids 12: II – 233. | en_US |
dc.identifier.citedreference | Berner J, Shutts GJ, Leutbecher M, Palmer TN. 2009. A spectral stochastic kinetic energy backscatter scheme and its impact on flow‐dependent predictability in the ECMWF ensemble prediction system. J. Atmos. Sci. 66: 603 – 625. | en_US |
dc.identifier.citedreference | Bowler NE, Arribas A, Beare SE, Mylne KR, Shutts GJ. 2009. The Local ETKF and SKEB: upgrades to the MOGREPS short‐range ensemble prediction system. Q. J. R. Meteorol. Soc. 135: 767 – 776. | en_US |
dc.identifier.citedreference | Brown AR, MacVean MK, Mason PJ. 2000. The effects of numerical dissipation in large eddy simulations. J. Atmos. Sci. 57: 3337 – 3348. | en_US |
dc.identifier.citedreference | Chen S, Ecke RE, Eyink GL, Wang X, Xiao Z. 2003. Physical mechanism of the two‐dimensional enstrophy cascade. Phys. Rev. Lett. 91: 215401‐1 – 215401‐4. | en_US |
dc.identifier.citedreference | Chen S, Ecke RE, Eyink GL, Wang X, Xiao Z. 2006. Physical mechanism of the two‐dimensional inverse energy cascade. Phys. Rev. Lett. 96: 084502‐1 – 084502‐4. | en_US |
dc.identifier.citedreference | Domaradski JA, Saiki EM. 1997. Backscatter models for large‐eddy simulations. Theoret. Comput. Fluid Dynamics 9: 75 – 83. | en_US |
dc.identifier.citedreference | Durran DR. 1999. Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer: Berlin. | en_US |
dc.identifier.citedreference | Frederiksen JS, Kepert SM. 2006. Dynamical subgrid‐scale parameterizations from direct numerical simulations. J. Atmos. Sci. 63: 3006 – 3019. | en_US |
dc.identifier.citedreference | Grinstein FF, Margolin LG, Rider W. 2007. Implicit Large Eddy Simulation. Cambridge University Press: Cambridge, UK. | en_US |
dc.identifier.citedreference | Jablonowski C, Williamson DL. 2011. The pros and cons of diffusion, filters and fixers in atmospheric general circulation models. In Numerical Techniques for Global Atmospheric Models, Lauritzen PH, Jablonowski C, Taylor MA, Nair RD (eds). Springer: Berlin; 381 – 493. | en_US |
dc.identifier.citedreference | Kent J, Thuburn J, Wood N. 2012. Assessing implicit large eddy simulation for two‐dimensional flow. Q. J. R. Meteorol. Soc. 138: 365 – 376. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.