Low dimensional attractors arise from forcing at small scales
UNSPECIFIED (2003) Low dimensional attractors arise from forcing at small scales. PHYSICA D-NONLINEAR PHENOMENA, 181 (1-2). pp. 39-44. ISSN 0167-2789Full text not available from this repository.
Official URL: http://dx.doi.org/10.1016/S0167-2789(03)00096-4
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|
|Subjects:||Q Science > QA Mathematics
Q Science > QC Physics
|Journal or Publication Title:||PHYSICA D-NONLINEAR PHENOMENA|
|Publisher:||ELSEVIER SCIENCE BV|
|Date:||1 July 2003|
|Number of Pages:||6|
|Page Range:||pp. 39-44|
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