The navier-stokes-α equations revisited

Geophysical and Astrophysical Fluid Dynamics

Volumn 103, Issue 4, 2009, Pages 303-316

  Roberts, Paul H ^a   Soward, Andrew M ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

Euler's equation; Hybrid euler lagrange description; Kelvin's circulation theorem; Sub grid scales

Indexed keywords

DIRECT APPROACH; EULER'S EQUATION; FLUID FLOW; HAMILTON'S PRINCIPLE; KELVIN'S CIRCULATION THEOREM; LAGRANGE DESCRIPTION; MODEL EQUATIONS; NAVIER STOKES; SUBGRID SCALE; TAYLOR HYPOTHESIS;

EULER EQUATIONS; LAGRANGE MULTIPLIERS; TURBULENT FLOW;

NAVIER STOKES EQUATIONS;

EULERIAN ANALYSIS; FLOW MODELING; FLOW VELOCITY; FLUID FLOW; LARGE EDDY SIMULATION; NAVIER-STOKES EQUATIONS;

EID: 74749091712     PISSN: 03091929     EISSN: 10290419     Source Type: Journal    
DOI: 10.1080/03091920902765638     Document Type: Article

References (18)

1. Andrews, D.G. and McIntyre, M.E., An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 1978, 89, 609-646.
2. Berselli, L.C., Illiescu, T. and Layton, W.J., Mathematics of Large Eddy Simulation of Turbulent Flows, p. 348, 2006 (Springer: Berlin).
3. Chen, S.Y., Holm, D.D., Margolin, G. and Zhang, R., Direct numerical simulations of the Navier-Stokes alpha model. Physica D 1999c, 133, 66-83.
4. Foias, C., Holm, D.D. and Titi, E.S., The Navier-Stokes-α model of fluid turbulence. Physica D 2001, 152, 505-519.
5. Frieman, E. and Rotenberg, M., On hydromagnetic stability of stationary equilibria. Rev. Mod. Phys. 1960, 32, 898-902.
6. Geurts, B.J. and Holm, D.D., Regularization modeling for large-eddy simulation. Phys. Fluids 2003, 15, L13-L16.
7. Geurts, B.J. and Holm, D.D., Leray and NS-a modeling of turbulent mixing. J. Turb. 2006, 7, 1-33.
8. Geurts, B.J., Kuczaj, A.K. and Titi, E.S., Regularization modeling for large-eddy simulation of homogeneous isotropic decaying turbulence. J. Phys. A: Math. Theor. 2008, 41, 344008.
9. Glatzmaier, G.A. and Roberts, P.H., A three-dimensional self-consistent computer simulation of the geomagnetic field. Nature 1995, 377, 203-209.
10. Holm, D.D., Lagrangian averages, averaged Lagrangians, and the mean effect of fluctuations in fluid dynamics. Chaos 2002a, 12, 518-530.
11. Holm, D.D., Averaged Lagrangians and mean effects of fluctuations in ideal fluid dynamics. Physica D 2002b, 170, 253-286.
12. Ilyin, A., Lunasin, E. and Titi, E.S., A modified-Leray-a subgrid scale model of turbulence. Nonlinearity 2006,19,879-897.
13. Jones, C.A. and Roberts, P.H., Turbulence models and plane layer dynamos, Fluid dynamics and dynamos in astrophysics and geophysics. In The Fluid Mechanics of Astrophysics and Geophysics (Series Edited by A.M. Soward and M. Ghil), edited by A.M. Soward, C.A. Jones, D.W. Hughes and N.O. Weiss, Vol. 12, pp. 295-330, 2005 (CRC Press: Florida).
14. Meneveau, C. and Katz, J., Scale-invariance and turbulence models for large-eddy simulation. Ann. Rev. Fluid Mech. 2000, 32, 1-32.
15. Roberts, P.H. and Soward, A.M., Eulerian and Lagrangian means in rotating magnetohydrodynamic flows I. General results. Geophys. Astrophys. Fluid Dynam. 2006a, 100, 457-483.
16. Roberts, P.H. and Soward, A.M., Covariant description of non-relativistic magnetohydrodynamics. Geophys. Astrophys. Fluid Dynam. 2006b, 100, 485-502.
17. Soward, A.M., A kinematic theory of large magnetic Reynolds number dynamos. Phil. Trans. R. Soc. Lond. A 1972, 272, 431-462.
18. Soward, A.M. and Roberts, P.H., On the derivation of the Navier-Stokes-α equations from Hamilton's Principle. J. Fluid Mech. 2008, 604, 297-323.