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Turbulent transition in a truncated one-dimensional model for shear flow


Reference:

Dawes, J. H. P. and Giles, W. J., 2011. Turbulent transition in a truncated one-dimensional model for shear flow. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 467 (2135), pp. 3066-3087.

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Official URL:

http://dx.doi.org/10.1098/rspa.2011.0225

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Abstract

We present a reduced model for the transition to turbulence in shear flow that is simple enough to admit a thorough numerical investigation, while allowing spatio-temporal dynamics that are substantially more complex than those allowed in previous modal truncations. Our model allows a comparison of the dynamics resulting from initial perturbations that are localized in the spanwise direction with those resulting from sinusoidal perturbations. For spanwise-localized initial conditions, the subcritical transition to a 'turbulent' state (i) takes place more abruptly, with a boundary between laminar and turbulent flows that appears to be much less 'structured' and (ii) results in a spatio-temporally chaotic regime within which the lifetimes of spatio-temporally complicated transients are longer, and are even more sensitive to initial conditions. The minimum initial energy E(0) required for a spanwise-localized initial perturbation to excite a chaotic transient has a power-law scaling with the Reynolds number E(0) similar to Re(p) with p approximate to -4.3. The exponent p depends only weakly on the width of the localized perturbation and is lower than that commonly observed in previous low-dimensional models where typically p approximate to -2. The distributions of lifetimes of chaotic transients at the fixed Reynolds number are found to be consistent with exponential distributions.

Details

Item Type Articles
CreatorsDawes, J. H. P.and Giles, W. J.
DOI10.1098/rspa.2011.0225
Related URLs
URLURL Type
http://arxiv.org/abs/1107.0580v1Free Full-text
Uncontrolled Keywordsdynamical systems, fluid flow, turbulence
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code26567

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