Stochastic differential equation modeled on a turbulent thermal convection field

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The noisy Burgers equation (NBE) modeled on the Kuramoto-Sivashinky equation (KSE) has two coefficients of an effective viscosity nu_eff and a noise strength N. In this study, they are optimized by the numerical stochastic integration of NBE to recover the properties of KSE. Under the condition that the average and variance of the solution of NBE agree with those of KSE, the values of the two coefficients are found to have a degree of freedom, showing exponential manner for a wide range of nu_eff. Their optimal values are determined by the agreement of large deviation functions obtained from the solutions of KSE and NBE. The optimal value of nu_eff, far smaller than known values, is found to accord with the estimated one by the Kalman-Bucy filter, minimizing the noise level N on the exponential curve. The agreement numerically validates the Yakhot conjecture. The strength N estimated by the variance of a noise-related term of KSE agrees well with the optimal one near nu_eff/alpha=1.