1997/06/18 by Xiaojun Li, Xiao-jun Li, Li, Xiao-jun +5
Computer Science · Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #chao-dyn #cond-mat.stat-mech #nlin.CD #nlin.PS #patt-sol #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.patt-sol/9706007
19 pages, 3 figures and 2 tables
arxiv created 1997/06/18 · openalex publication_date 1997/06/18 · openalex created_date 2016/06/24 · arxiv updated 2016/09/07 · openalex updated_date 2026/07/28
We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure factor S(k) with respect to the correlation length ξ2. We hence obtain analytical results for the time-averaged convective current J and the time-averaged vorticity current Ω. We also define power-law behaviors such as J ∼ εμ, Ω∼ ελ and ξ2 ∼ ε-ν, where ε is the control parameter. We find from our theory that μ= 1, ν≥ 1/2 and λ= 2 μ+ ν for phase turbulence and that μ= 1, ν≥ 1/2 and λ= 2 μ+ 2 ν for spiral-defect chaos. These predictions, together with the scaling conjecture for S(k), are confirmed by our numerical results. Finally we suggest that Porod's law, S(k) ∼ 1/ξ2 k3 for large k, might be valid in STC.