A study of the Navier-Stokes-alpha model for two-dimensional turbulence

• Main Authors: Lunasin, E, Kurien, S, Taylor, M, Titi, E
• Format: Journal Article
• Language: English
• Published: 22-02-2007
• Subjects: Physics - Chaotic Dynamics; Physics - Fluid Dynamics
• DOI: 10.48550/arxiv.physics/0702196

For wavenumbers k such that k * alpha > 1, corresponding to spatial scales
smaller than alpha, there are three candidate power laws for the energy
spectrum of the Navier-Stokes-alpha model, corresponding to three possible
dynamical eddy turnover time scales in the model equations: one from the
smoothed field, the second from the rough field and the third from a special
combination of the two. Using two-dimensional turbulence as a test case, we
measure the scaling of the spectra from high-resolution simulations of the
Navier-Stokes-alpha model, in the limit as alpha goes to infinity. We show that
the energy spectrum of the smoothed velocity field scales as k^{-7} in the
direct enstrophy cascade regime, consistent with dynamics dominated by the time
scale of the rough velocity field.