A geometrical study of 3D incompressible Euler flows with Clebsch potentials - a long-lived Euler flow and its power-law energy spectrum

Physica D: Nonlinear Phenomena

Volumn 237, Issue 14-17, 2008, Pages 2020-2027

  Ohkitani, Koji ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Euler equations; Numerical simulation; Onsager conjecture; Regularity

Indexed keywords

COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; ENERGY DISSIPATION; EULER EQUATIONS; VORTICITY;

ENERGY SPECTRA; INITIAL CONDITIONS; INVISCID LIMITS; NAVIER STOKES FLOW; ONSAGER; POWER LAW SPECTRUM; REGULARITY; VORTICITY LAYERS;

NAVIER STOKES EQUATIONS;

EID: 47049095872     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2008.01.011     Document Type: Article

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22. This expression is naive as it involves dual limits; small viscosity and large time, which are not interchangeable in general. We will be more specific, where necessary
23. 2 at a higher end of wavenumber) [7,8]
24. 2 + ∇ ψ
25. For n pairs of Clebsch potentials plus a solenoidal projector
26. For such a expression to be valid globally, we need a Frobenius condition of integrability. Thus, actually it restricts us to a very special class of flows