2000/08/10 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 and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #nlin.CD #nlin.PS
paper · pdf · doi:10.48550/arxiv.cond-mat/0008173
Submitted
arxiv created 2000/08/10 · openalex publication_date 2000/08/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a phenomenological theory for phase turbulence (PT) in Rayleigh-Bénard convection, based on the generalized Swift-Hohenberg model. We apply a Hartree-Fock approximation to PT and conjecture a scaling form for the structure factor S(k) with respect to the correlation length ξ2. We hence obtain \it analytical results for the time-averaged convective current J and the time-averaged mean square vorticity 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. These predictions, together with the scaling conjecture for S(k), are confirmed by our numerical results.