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Low dimensional attractors arise from forcing at small scales
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UNSPECIFIED (2003) Low dimensional attractors arise from forcing at small scales. PHYSICA D-NONLINEAR PHENOMENA, 181 (1-2). pp. 39-44. doi:10.1016/S0167-2789(03)00096-4 ISSN 0167-2789.
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Official URL: http://dx.doi.org/10.1016/S0167-2789(03)00096-4
Abstract
Standard estimates of the dimension of the attractor of the 2D Navier-Stokes equations are given in terms of a dimensionless Grashof number that measures the total amount of energy injected into the flow. However, this result takes no I account of whether the forcing is concentrated at large or small scales. By a simple modification of the usual argument, this paper provides a bound that is linear in a modified Grashof number that reflects the spatial structure of the forcing. In particular, as a fixed amount of energy is injected at progressively smaller scales then the dimension of the attractor decreases. (C) 2003 Elsevier Science B.V. All rights reserved.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | PHYSICA D-NONLINEAR PHENOMENA | ||||
Publisher: | ELSEVIER SCIENCE BV | ||||
ISSN: | 0167-2789 | ||||
Official Date: | 1 July 2003 | ||||
Dates: |
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Volume: | 181 | ||||
Number: | 1-2 | ||||
Number of Pages: | 6 | ||||
Page Range: | pp. 39-44 | ||||
DOI: | 10.1016/S0167-2789(03)00096-4 | ||||
Publication Status: | Published |
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