KDV-BURGERS EQUATION MODELING OF TURBULENCE

The idea, suggested by Gao Ge in 1985, that KdV-Burgers equation can be regarded as the normal equation of turbulence is shown to be meaningful by the present paper using the travelling wave analytic solution of KdV-Burgers equation. By analyzing the cascading down process of turbulence, it is pointed out that the process proceeds on a geometrical series with a common ratio due to the intermittence of turbulence. The energy spectrum of turbulence is obtained from the perturbation velocity solution of KdV-Burgers equation. The slope of energy spectrum lies between -1.76 and -1.97 in the dilogarithmic coordinate paper. The corresponding fractual dimensions lie between 2.09 and 2.72 in terms of intermittency turbulence model by Frisch (1978). The physical mechanism of dissipation and dispersion effects for turbulence is discussed by means of atmospheric dynamics.