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

TitleGoing to new lengths: Studying the Navier-Stokes-αβ equations using the strained spiral vortex model
Publication TypeJournal Article
Year of Publication2014
AuthorsTY Kim, X Chen, JE Dolbow, and E Fried
JournalDiscrete and Continuous Dynamical Systems Series B
Volume19
Start Page2207
Issue7
Pagination2207 - 2225
Date Published01/2014
Abstract

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.

DOI10.3934/dcdsb.2014.19.2207
Short TitleDiscrete and Continuous Dynamical Systems Series B