Going to new lengths: Studying the Navier-Stokes-αβ equations using the strained spiral vortex model


Journal Article

We study the effect of the length scales α and β on the performance of the Navier-Stokes-αβ equations for numerical simulations of turbulence over coarse discretizations. To this end, we rely on the strained spiral vortex model and take advantage of the dimensional reduction allowed by that model. In particular, the three-dimensional energy spectrum is reformulated so that it can be calculated from solutions of the two-dimensional unstrained Navier-Stokes-αβ equations. A similarity theory for the spiral vortex model shows that the Navier-Stokes-αβ model is better equipped than the Navier-Stokes-α model to capture smaller-scale behavior. Numerical experiments performed using a pseudo-spectral discretization along with the second-order Adams-Bashforth time-stepping algorithm yield results indicating that the fidelity of the energy spectrum in both the inertial and dissipation ranges is significantly improved for β < α.

Full Text

Duke Authors

Cited Authors

  • Kim, TY; Chen, X; Dolbow, JE; Fried, E

Published Date

  • January 1, 2014

Published In

Volume / Issue

  • 19 / 7

Start / End Page

  • 2207 - 2225

International Standard Serial Number (ISSN)

  • 1531-3492

Digital Object Identifier (DOI)

  • 10.3934/dcdsb.2014.19.2207

Citation Source

  • Scopus