Solitary-wave solutions of the Navier-Stokes equation

将涨落关联的经典湍流理论中引入的分离变量方法应用于具有密度变化和化学反应的非均匀湍流。导出了一个由一个控制平均热力/气动力量的雷诺平均方程和另一个控制涨落关联的方程组成的方程组，每个方程都通过湍流输运项耦合。将所提出的公式应用于预测火焰在湍流预混气体中的传播速度和预测Benard对流的Nusselt数问题。对于前者，该方程组构成了一个以火焰速度为特征值的特征值问题，与湍流输运同时确定。对不同湍流强度的甲烷空气预混气体在未燃烧状态下的火焰速度进行了计算，并与已有的实验进行了比较，也与重整化群理论的预测结果进行了比较，结果与实验吻合较好。应用于Benard对流的高瑞利数区(Ra&Gt；5×10^5)，预测了平均温度分布和总的湍流换热(Nusselt数)。考虑到该理论不包括任何经验参数，这与现有的实验是令人满意的。通过逆傅立叶变换得到了功率谱。

A method of separation of variables introduced in the classical turbulence theory of fluctuation correlations is applied to inhomogeneous turbulence with density variation and chemical reactions. A system of equations consisting of the one governing mean thermo / gasdynamic quantities, namely, the Reynolds-averaged equations, and the other governing fluctuation correlations, each coupled through turbulent transport terms, are derived. The proposed formalism is applied to the problem of predicting velocity of a flame propagating In a turbulent premixed gas and of predicting Nusselt number of the Benard convection. Regarding the former, the system of equations constitutes an eigenvalue problem with the flame velocity as the eigenvalue, to be determined simultaneously with turbulent transports. Flame velocities calculated for a methaneair premixtare with varied turbulence intensities given at unburnt state are compared with existing experiments also with prediction by the renormalization group theory, and excellent agreement with experiment is observed. The application to the latter, namely high Rayleigh number regime(Ra> 5xlO^5)of Benard convection predicts the mean temperature distribution and the total turbulent heat transfer(the Nusselt number). The agreement is with existing experiment satisfactory considering that the theory does not include any empirical parameters. Power spectrum is also obtained through inverse-Fourier transform.