2015
DOI: 10.1017/jfm.2015.596
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Disruption of states by a stable stratification

Abstract: We identify 'minimal seeds' for turbulence, i.e. initial conditions of the smallest possible total perturbation energy density E c that trigger turbulence from the laminar state, in stratified plane Couette flow, the flow between two horizontal plates of separation 2H, moving with relative velocity 2 U, across which a constant density difference 2 ρ from a reference density ρ r is maintained. To find minimal seeds, we use the 'direct-adjoint-looping' (DAL) method for finding nonlinear optimal perturbations tha… Show more

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Cited by 25 publications
(28 citation statements)
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“…In the critical layer, stratification needs to be Figure 20 (left) confirms this scaling as Ri b increases from zero which is just a statement that the Rayleigh number, Ra := −Ri b Re 2 P r, is O(1). This scaling was proposed by Eaves & Caulfield (2015) by heuristic arguments and has also been independently found recently by Deguchi (2017).…”
Section: )supporting
confidence: 75%
“…In the critical layer, stratification needs to be Figure 20 (left) confirms this scaling as Ri b increases from zero which is just a statement that the Rayleigh number, Ra := −Ri b Re 2 P r, is O(1). This scaling was proposed by Eaves & Caulfield (2015) by heuristic arguments and has also been independently found recently by Deguchi (2017).…”
Section: )supporting
confidence: 75%
“…, equivalent to the Rayleigh number Ra −Ri b PrRe 2 being O(1), was first observed numerically in the Pr = 1 case by Eaves & Caulfield (2015) and then in the analysis of Deguchi (2017) and Olvera & Kerswell (2017). There, at least for Pr = O(1), once the stratification strength increases beyond this scaling, new dynamic balances emerge [e.g.…”
Section: Low Prandtl Number (Pr 1)mentioning
confidence: 98%
“…Pringle et al (2012) argue for why energy growth after time T might be the most natural objective functional for this procedure, but actually any objective functional which takes on heightened values in the basin of attraction of the turbulent state will do (e.g. total dissipation over the trajectory -Monokrousos et al 2011, Duguet et al 2013and Eaves & Caulfield 2015. The key point is that the optimization procedure should seek out any initial condition on the energy hypersurface which is in the turbulent basin of attraction if such states maximise the objective functional.…”
Section: Switching Basins Of Attraction: Minimal Seeds For Transitionmentioning
confidence: 99%