Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence

References

• Kolmogorov AN. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc R Soc A Math Phys Eng Sci. 1991;434(1890):9–13.
   Web of Science ®Google Scholar
• Brasseur JG, Corrsin S. Spectral evolution of the Navier–Stokes equations for low order couplings of Fourier modes. Berlin: Springer; 1987. p. 152–162.
   Google Scholar
• Brasseur JG, Yeung PK. Large and small-scale coupling in homogeneous turbulence - analysis of the Navier–Stokes equation in the asymptotic limit. In: Durst F, Friedrich R, Launder BE, Schmidt FW, Schumann U, Whitelaw JH, editors. 8th Symposium on turbulent shear flows. Vol. 1, Thin solid films. Munich: Springer-Verlag; 1991.
   Google Scholar
• Yeung PK, Brasseur JG. The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys Fluids A Fluid Dyn. 1991;3(5):884–897.
   Google Scholar
• Pumir A. Turbulence in homogeneous shear flows. Phys Fluids. 1996;8:3112.
   Web of Science ®Google Scholar
• Pumir A, Shraiman BI. Persistent small scale anisotropy in homogeneous shear flows. Phys Rev Lett. 1995;75:3114.
   PubMed Web of Science ®Google Scholar
• Shen X, Warhaft Z. The anisotropy of the small scale structure in high Reynolds number (Rλ ∼ 1000) turbulent shear flow. Phys Fluids. 2000;12:2976.
   Web of Science ®Google Scholar
• Yeung PK, Brasseur JG, Wang Q. Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views. J Fluid Mech. 1995;283:43–95.
   Web of Science ®Google Scholar
• Delache A, Cambon C, Godeferd F. Scale by scale anisotropy in freely decaying rotating turbulence. Phys Fluids. 2014;26(2):025104.
   Web of Science ®Google Scholar
• Eswaran V, Pope SB. An examination of forcing in direct numerical simulations of turbulence. Comput Fluids. 1988;16(3):257–278.
   Web of Science ®Google Scholar
• Sullivan NP, Mahalingam S, Kerr RM. Deterministic forcing of homogeneous, isotropic turbulence. Phys Fluids. 1994;6(4):1612–1614.
   Web of Science ®Google Scholar
• Alvelius K. Random forcing of three-dimensional homogeneous turbulence. Phys Fluids. 1999;11(7):1880–1889.
   Web of Science ®Google Scholar
• Jiménez J, Wray AA, Saffman PG, et al. The structure of intense vorticity in isotropic turbulence. J Fluid Mech. 1993;255:65–90.
   Web of Science ®Google Scholar
• Pumir A. A numerical study of pressure fluctuations in three-dimensional, incompressible, homogeneous, isotropic turbulence. Phys Fluids. 1994;6(6):2071–2083.
   Web of Science ®Google Scholar
• Mininni PD, Pouquet A. Helicity cascades in rotating turbulence. Phys Rev E. 2009;79:026304.
   Web of Science ®Google Scholar
• Sen A, Mininni PD, Rosenberg D, et al. Anisotropy and nonuniversality in scaling laws of the large-scale energy spectrum in rotating turbulence. Phys Rev E. 2012;86:036319.
   Web of Science ®Google Scholar
• Mordant N, Pinton J-F, Chillà F. Characterization of turbulence in a closed flow. J Phys II France. 1997;7(11):1729–1742.
   Google Scholar
• Godeferd F, Moisy F. Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. ASME Appl Mech Rev. 2015;67(3): 030802–030802–13 .
   Web of Science ®Google Scholar
• Zeman O. A note on the spectra and decay of rotating homogeneous turbulence. Phys Fluids. 1994;6:3221.
   Web of Science ®Google Scholar
• Woods JD. Diffusion due to fronts in the rotation sub-range of turbulence in the seasonal thermocline. La Houille Blanche. 1974;29:589–597.
   Google Scholar
• Vassilicos J. Dissipation in turbulent flows. Palo Alto (CA): Annual Reviews; 2015. p. 95–114.
   Google Scholar
• Bos WJ, Shao L, Bertoglio J-P. Spectral imbalance and the normalized dissipation rate of turbulence. Phys Fluids. 2007;19(4):045101.
   Web of Science ®Google Scholar
• Goto S, Vassilicos J. Energy dissipation and flux laws for unsteady turbulence. Phys Lett A. 2015;379(16–17):1144–1148.
   Web of Science ®Google Scholar
• Mininni PD, Rosenberg D, Pouquet A. Isotropization at small scales of rotating helically driven turbulence. J Fluid Mech. 2012;699:263–279.
   Web of Science ®Google Scholar
• Kaneda Y, Ishihara T. High-resolution direct numerical simulation of turbulence. J Turbul. 2006;7:N20.
   Web of Science ®Google Scholar
• Lumley JL, Newman GR. The return to isotropy of homogeneous turbulence. J Fluid Mech. 1977;82(1):161–178.
   Google Scholar
• Lamriben C, Cortet P-P, Moisy F. Direct measurements of anisotropic energy transfers in a rotating turbulence experiment. Phys Rev Lett. 2011;107:024503.
   PubMed Web of Science ®Google Scholar
• Kurien S. Anisotropy and the universal properties of turbulence [dissertation]. New Haven (CT): Yale University; 2001.
   Google Scholar
• Craya A. Contribution à l’analyse de la turbulence associée à des vitesses moyennes [Contribution to the analysis of turbulence with mean velocities]. PST no. 345. Paris: Ministère de l’Air; 1958. p. 345.
   Google Scholar
• Sagaut P, Cambon C. Homogeneous turbulence dynamics. New York (NY): Cambridge University Press; 2008.
   Google Scholar
• Cambon C, Mansour NN, Godeferd FS. Energy transfer in rotating turbulence. J Fluid Mech. 1997;337:303.
   Web of Science ®Google Scholar
• Waleffe F. Inertial transfers in the helical decomposition. Phys Fluids A Fluid Dyn. 1993;5(3):677–685.
   Web of Science ®Google Scholar
• Favier B, Godeferd FS, Cambon C, et al. Quasi-static magnetohydrodynamic turbulence at high Reynolds number. J Fluid Mech. 2011;681:434–461.
   Web of Science ®Google Scholar
• Moffatt HK. The degree of knottedness of tangled vortex lines. J Fluid Mech. 1969;35(1):117–129.
   Google Scholar
• Moffatt HK, Tsinober A. Helicity in laminar and turbulent flow. Ann Rev Fluid Mech. 1992;24(1):281–312.
   Google Scholar
• Galtier S. Theory for helical turbulence under fast rotation. Phys Rev E. 2014;89:041001.
   Web of Science ®Google Scholar
• Godeferd FS, Staquet C. Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy. J Fluid Mech. 2003;486:115–159.
   Web of Science ®Google Scholar
• Cambon C, Jacquin L. Spectral approach to non-isotropic turbulence subjected to rotation. J Fluid Mech. 1989;202:295–317.
   Web of Science ®Google Scholar
• Orszag SA, Patterson GS. Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys Rev Lett. 1972;28:76–79.
   Web of Science ®Google Scholar
• Vincent A, Meneguzzi M. The spatial structure and statistical properties of homogeneous turbulence. J Fluid Mech. 1991;225:1–20.
   Web of Science ®Google Scholar
• Mathieu J, Scott J. An introduction to turbulent flow. New York (NY): Cambridge University Press; 2000.
   Google Scholar
• Kreuzahler S, Schulz D, Homann H, et al. Numerical study of impeller-driven von Karman flows via a volume penalization method. New J Phys. 2014;16:103001.
   Web of Science ®Google Scholar
• Brummell NH, Cattaneo F, Tobias SM. Linear and nonlinear dynamo properties of time-dependent abc flows. Fluid Dyn Res. 2001;28(4):237.
   Web of Science ®Google Scholar
• Childress S, Gilbert AD. Stretch, twist, fold: the fast dynamo. Vol. 37, Lecture Notes in Physics monographs. Berlin: Springer; 1995.
   Google Scholar
• Rosenberg DL, Marino R, Mininni P, et al. Inverse energy cascades in rotating turbulence. In Proceedings, abstract number NG14A-02 in Fall meeting. Washington (DC): American Geophysical Union; 2013.
   Google Scholar
• Cichowlas C, Bonaïti P, Debbasch F, et al. Effective dissipation and turbulence in spectrally truncated Euler flows. Phys Rev Lett. 2005;95:264502.
   PubMed Web of Science ®Google Scholar
• Kraichnan RH. Helical turbulence and absolute equilibrium. J Fluid Mech. 1973;59(4):745–752.
   Google Scholar
• Naso A, Godeferd FS. Statistics of the perceived velocity gradient tensor in a rotating turbulent flow. New J Phys. 2012;14(12):125002.
   Google Scholar
• Meldi M, Sagaut P. Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay. J Fluid Mech. 2017;818:697–715.
   Web of Science ®Google Scholar
• Thornber B. Impact of domain size and statistical errors in simulations of homogeneous decaying turbulence and the Richtmyer–Meshkov instability. Phys Fluids. 2016;28(4):045106.
   Web of Science ®Google Scholar
• Mininni PD, Alexakis A, Pouquet A. Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws. Phys Rev E. 2008;77:036306.
   Web of Science ®Google Scholar
• Baqui YB, Davidson PA. A phenomenological theory of rotating turbulence. Phys Fluids. 2015;27(2):025107.
   Web of Science ®Google Scholar