On the smallest scale for the incompressible Navier-Stokes equations | Zendy

William D. Henshaw | Zendy; H.- Kreiss | Zendy; Luis G. Reyna | Zendy

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On the smallest scale for the incompressible Navier-Stokes equations

Author(s) -

William D. Henshaw,

H.- Kreiss,

Luis G. Reyna

Publication year - 1989

Publication title -

theoretical and computational fluid dynamics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.817

H-Index - 59

eISSN - 1432-2250

pISSN - 0935-4964

DOI - 10.1007/bf00272138

Subject(s) - mathematics , compressibility , reynolds number , scale (ratio) , mathematical analysis , square root , length scale , reynolds averaged navier–stokes equations , navier–stokes equations , stokes' law , computational science and engineering , kinematics , stokes number , square (algebra) , stokes flow , physics , mechanics , geometry , computational fluid dynamics , classical mechanics , turbulence , flow (mathematics) , quantum mechanics

We prove that, for solutions to the two- and three-dimensional incompressible Navier-Stokes equations, the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two-dimensional flows, but have to be assumed in three dimensions. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result, to the decay rate of the energy spectrum are discussed.

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