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- W806076995 abstract "Many realised in the 1980s that Chaos theory was not going to solve the problem of turbulence because it is an inherently spatiotemporal phenomenon (at least at low to intermediate Re). Pomeau [12]1 was the first to start thinking about turbulence from a statistical mechanical viewpoint by comparing spatiotemporal intermittency to directed percolation. Here, a spatial lattice of sites which individually can either be active (‘turbulent’) or passive (‘laminar’) is stochastically evolved in time using simple rules which incorporate information about neighbouring states. In the simplest models, there is one parameter p which defines the evolutionary strategy and then the challenge is to characterise the ensuing dynamics as a function of p. What typically emerges is that the order parameter ρ(t) defined as the ensemble average of the lattice average of active sites (active=1, passive =0) asymptotes to 0 as t → ∞ for p ≤ pc where pc is a critical value, whereas for p > pc, limt→∞ ρ(t) ∼ (p−pc) β" @default.
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- W806076995 date "2011-01-01" @default.
- W806076995 modified "2023-09-27" @default.
- W806076995 title "Lecture 10: Turbulence: Transient or Sustained?" @default.
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