Gibbon, J. D. A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations. (English) Zbl 1291.35181 Commun. Math. Sci. 10, No. 1, 131-136 (2012). Summary: Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stokes equations on a periodic box. The estimate for the smallest of these inverse scales coincides with the inverse Kolmogorov length, but thereafter the exponents of the Reynolds number rise rapidly for correspondingly higher moments. The implications of these results for the computational resolution of small scale vortical structures are discussed. Cited in 5 Documents MSC: 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:Navier-Stokes; weak solutions; moments of vorticity; inverse length scales PDFBibTeX XMLCite \textit{J. D. Gibbon}, Commun. Math. Sci. 10, No. 1, 131--136 (2012; Zbl 1291.35181) Full Text: DOI arXiv