The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and ...The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.展开更多
Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, ...Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).展开更多
基金The work is supported by the National Basic Research Program "Non-linear Sciences the National Natural Science Foundation of China
文摘The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.
基金The project supported by the National Basic Research Program "Non-linear Science"
文摘Using nonequilibrium statistical mechanics closure method, it is shown that the skewness factor of the velocity derivative of isotropic turbulence ap- proaches a constant -0.515 when the Reynolds number is very high, which is in agree- ment with the DNS (direct numerical simulation) result of Vincent and Meneguzzi (1991).
