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Turbulent transition in a truncated one-dimensional model for shear flow
- Publication Year :
- 2011
-
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 localised in the spanwise direction with those resulting from sinusoidal perturbations. For spanwise-localised initial conditions the subcritical transition to a `turbulent' state (i) takes place more abruptly, with a boundary between laminar and `turbulent' flow that is appears to be much less `structured' and (ii) results in a spatiotemporally chaotic regime within which the lifetimes of spatiotemporally complicated transients are longer, and are even more sensitive to initial conditions. The minimum initial energy $E_0$ required for a spanwise-localised initial perturbation to excite a chaotic transient has a power-law scaling with Reynolds number $E_0 \sim Re^p$ with $p \approx -4.3$. The exponent $p$ depends only weakly on the width of the localised perturbation and is lower than that commonly observed in previous low-dimensional models where typically $p \approx -2$. The distributions of lifetimes of chaotic transients at fixed Reynolds number are found to be consistent with exponential distributions.<br />Comment: 22 pages. 11 figures. To appear in Proc. Roy. Soc. A
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1107.0580
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1098/rspa.2011.0225