A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations

Details A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations A hierarchy of length scales for weak solutions of the three-dimensional Navier-Stokes equations

2010-12-16

arxiv.org/abs/1012.3604v2

Nonlinear Sciences

Chaotic Dynamics

Dedicated to David Levermore on the occasion of his 60th birthday. To appear in Comm. Math. Sci. (version 2)

Scientific paper

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.

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