Theory for the rotational deconvolution model of turbulence with fractional regularization

References

• Chen S, Foias C, Holm D, Olson E, Titi ES, Wynne S. The Camassa-Holm equations and turbulence. Physica D. 1999;D133:49–65.
   Web of Science ®Google Scholar
• Foias C, Holm D, Titi ES. The three dimensional viscous Camassa-Holm equations and their relation to the Navier-Stokes equations and turbulence theory. Journal of Dynamics and Differential Equations. 2002;14:1–35.
   Google Scholar
• Ilyin AA, Lunasin EM, Titi ES. A modified Leray-alpha subgrid-scale model of turbulence. Nonlinearity. 2006;19:879–897.
   Web of Science ®Google Scholar
• Cheskidov A, Holm DD, Olson E, Titi ES. On a Leray-α model of turbulence. Royal Society London, Proceedings, Series A, Mathematical, Physical and Engineering Sciences. 2005;461:629–649.
   Web of Science ®Google Scholar
• Cao Y, Lunasin EM, Titi ES. Globall well-posdness of the three dimensional viscous and inviscid simplified bardina turbulence models. Communications in Mathematical Sciences. 2006;4(4):823–848.
   Web of Science ®Google Scholar
• Rebholz LG. A family of new high order NS-α models arising from helicity correction in Leray turbulence models. Journal of Mathematical Analysis and Applications. 2008;342:246–254.
   Web of Science ®Google Scholar
• Layton W, Stanculescu I, Trenchea C. Theory of the NS-ω̅ model: a complement to the NS-α model. Communications on Pure and Applied Analysis. 2011;10:1763–1777.
   Web of Science ®Google Scholar
• Zhou Y, Fan J. On the Cauchy problem for a Leray-α-MHD model. Nonlinear Analysis: Real World Applications. 2011;12(1):648–657.
   Web of Science ®Google Scholar
• Zhou Y, Fan J. Regularity criteria for a Lagrangian-averaged magnetohydrodynamic-α model. Nonlinear Analysis. 2011;74:1410–1420.
   Web of Science ®Google Scholar
• Olson E, Titi ES. Viscosity versus vorticity stretching: global well-posdness for a family of Navier-Stokes-alpha-like models. Nonlinear Analysis. 2007;66:2427–2458.
   Web of Science ®Google Scholar
• Germano M. Differential filters for the large eddy simulation of turbulent flows. Physics of Fluids. 1986;29:1755–1757.
   Web of Science ®Google Scholar
• Bertero M, Boccacci B. Introduction to inverse problems in imaging. Bristol: IOP; 1998.
   Google Scholar
• Stolz S, Adams NA. An approximate deconvolution procedure for large-eddy simulation. Physics of Fluids. 1999;11:1699–1701.
   Web of Science ®Google Scholar
• Stolz S, Adams NA, Kleiser L. An approximate deconvolution model for large-eddy simulation with application to incompressible wall bounded flows. Physics of Fluids. 2001;13:997–1015.
   Web of Science ®Google Scholar
• Dunca A, Epshteyn Y. On the Stolz-Adams deconvolution model for the large-eddy simulation of turbulent flows. SIAM Journal on Mathematical Analysis. 2006;37(6):1890–1902.
   Web of Science ®Google Scholar
• Layton W, Lewandowski R. A simple and stable scale similarity model for large eddy simulation: energy balance and existence of weak solutions. Applied Mathematics Letters. 2003;16:1205–1209.
   Web of Science ®Google Scholar
• Layton W, Lewandowski R. On a well posed turbulence model. Continuous Dynamical Systems Series B. 2006;6(1):111–128.
   Web of Science ®Google Scholar
• Berselli LC, Lewandowski R. Convergence of ADMs to the mean Navier-Stokes equations. Annales de l’Institut Henri Poincare (C), NonLinear. Analysis. 2012;29:171–198.
   Google Scholar
• Ali H. Large eddy simulation for turbulent flows with critical regularization. Journal of Mathematical Analysis and Applications. 2012;394:291–304.
   Web of Science ®Google Scholar
• Layton W, Neda M. A similarity theory of approximate deconvolution models of turbulence. Journal of Mathematical Analysis and Applications. 2007;333:416–429.
   Web of Science ®Google Scholar
• Chow FK, Street RL, Xue M, Ferziger JH. Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow. Journal of the Atmospheric Sciences. 2005;62:2058–2077.
   Web of Science ®Google Scholar
• Dunca A, Lewandowski R. Modeling error in approximate deconvolution models. 2012. Available from: http://arxiv.org/abs/1111.6362
   Google Scholar
• Layton W, Manica CC, Neda M, Olshanskii M, Rebholz LG. On the accuracy of the rotation form in simulations of the Navier-Stokes equations. Journal of Computational Physics. 2009;228:3433–3447.
   Web of Science ®Google Scholar
• Ali H. On a critical Leray-α model of turbulence. Nonlinear Analysis: Real World Applications. 2013;14(3):1563–1584.
   Google Scholar
• Temam R. Navier-Stokes equations and nonlinear functional analysis. CBMS Regional Conference series, No. 41. Philadelphia (PA): SIAM; 1983.
   Google Scholar
• Wolfgang Walter. Differential and integral inequalities. Translated from the German by Lisa Rosenblatt and Lawrence Shampine. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 55. New York (NY): Springer-Verlag; 1970.
   Google Scholar
• Simon J. Compact sets in the spaces Lp (0, T; B). Annali Di Matematica Pura Ed Applicata. 1987;146:65–96.
   Web of Science ®Google Scholar