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http://hdl.handle.net/11375/16821
Title: | Controlling the dual cascade of two-dimensional turbulence |
Authors: | Farazmand, M. Kevlahan, N.K.-R. Protas, B. |
Keywords: | turbulence control;turbulence simulation;turbulence theory |
Publication Date: | 30-Nov-2010 |
Publisher: | Cambridge University Press |
Citation: | Farazmand, M.M., Kevlahan, N.K.-R. & Protas, P. 2011 Controlling the dual cascade of two-dimensional turbulence. J. Fluid Mech. 668, 202-222. |
Series/Report no.: | J. Fluid Mech.; |
Abstract: | The Kraichnan–Leith–Batchelor (KLB) theory of statistically stationary forced homogeneous isotropic two-dimensional turbulence predicts the existence of two inertial ranges: an energy inertial range with an energy spectrum scaling of k−5/3, and an enstrophy inertial range with an energy spectrum scaling of k−3. However, unlike the analogous Kolmogorov theory for three-dimensional turbulence, the scaling of the enstrophy range in the two-dimensional turbulence seems to be Reynolds-number- dependent: numerical simulations have shown that as Reynolds number tends to infinity, the enstrophy range of the energy spectrum converges to the KLB prediction, i.e. E ∼ k−3. The present paper uses a novel optimal control approach to find a forcing that does produce the KLB scaling of the energy spectrum in a moderate Reynolds number flow. We show that the time–space structure of the forcing can significantly alter the scaling of the energy spectrum over inertial ranges. A careful analysis of the optimal forcing suggests that it is unlikely to be realized in nature, or by a simple numerical model. |
URI: | http://hdl.handle.net/11375/16821 |
Identifier: | doi:10.1017/S0022112010004635 |
Appears in Collections: | Mathematics & Statistics Publications |
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main.pdf | Main file | 2.2 MB | Adobe PDF | View/Open |
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