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Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations

Gibbon, John D and Donzis, Diego A and Gupta, Anupam and Kerr, Robert M and Pandit, Rahul and Vincenzi, Dario (2014) Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations. In: NONLINEARITY, 27 (10). pp. 2605-2625.

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Official URL: http://dx.doi.org/ 10.1088/0951-7715/27/10/2605


The periodic 3D Navier-Stokes equations are analyzed in terms of dimensionless, scaled, L-2m-norms of vorticity D-m (1 <= m <= infinity). The first in this hierarchy, D-1, is the global enstrophy. Three regimes naturally occur in the D-1-D-m plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime 1]; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the IOP PUBLISHING LTD, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
Keywords: Navier-Stokes; regularity; turbulence
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 14 Nov 2014 07:27
Last Modified: 14 Nov 2014 07:27
URI: http://eprints.iisc.ac.in/id/eprint/50264

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