Solitary-wave solutions of the Navier-Stokes equation

将经典湍流涨落关联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/气动力学量的方程系统，即雷诺平均方程，和其他控制波动相关性，每个通过湍流输运项耦合。将所提出的形式应用于火焰在紊流预混气体中传播速度的预测和贝纳德对流的努塞尔数的预测。对于前者，方程组构成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。本文对不同湍流强度的甲烷-空气预混料在未燃烧状态下的火焰速度进行了计算，并与现有实验和重整化群论的预测结果进行了比较，结果与实验结果吻合较好。应用于后者，即贝纳德对流的高瑞利数区（Ra> 5xlO^5），可以预测平均温度分布和总湍流换热量（努塞尔数）。考虑到该理论不包含任何经验参数，该结果与现有实验结果一致，令人满意。通过傅里叶反变换得到功率谱。

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.