TY - JOUR
T1 - The one-point statistics of viscous Burgers turbulence initialized with Gaussian data
AU - Ryan, Reade
AU - Avellaneda, Marco
PY - 1999
Y1 - 1999
N2 - We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.
AB - We study the statistics of the viscous Burgers turbulence (BT) model, initialized at time t = 0 by a large class of Gaussian data. Using a first-principles analysis of the Hopf-Cole formula for the Burgers equation and the theory of large deviations for Gaussian processes, we characterize the tails of the probability distribution functions (PDFs) for the velocity u(x, t) and the velocity derivatives ∂nu(x,t)/∂xn,n = 1, 2, . . . . The PDF tails have a non-universal structure of the form log P(θ) ∝ -(Re)-ptqθr, where Re is the Reynolds number and p, q, and r depend on the order of differentiation and the infrared behavior of the initial energy spectrum.
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U2 - 10.1007/s002200050519
DO - 10.1007/s002200050519
M3 - Article
AN - SCOPUS:0033248331
SN - 0010-3616
VL - 200
SP - 1
EP - 23
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 1
ER -