Stochastic differential equation modeled on a turbulent thermal convection field

在Kuramoto-Sivashinky方程(KSE)的基础上建立的噪声Burgers方程(NBE)具有两个系数：有效粘度nu_ff和噪声强度N。本研究利用NBE的数值随机积分对它们进行优化，以恢复KSE的性质。在NBE的解的平均值和方差与KSE的解的平均值和方差一致的条件下，发现两个系数的值都具有一定的自由度，并且在较大的nUff范围内呈指数规律。它们的最佳值是由KSE和NBE解得到的大偏差函数的一致性决定的。Nu_ff的最优值远小于已知值，与Kalman-Bucy滤波的估计值相符，使指数曲线上的噪声水平N最小化。该协议从数字上证实了雅霍特猜想。由KSE的噪声相关项的方差估计的强度N与在Nu_Jeff/α=1附近的最佳强度N很好地吻合。

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.