KdV-BURGERS EQUATION MODELLING OF TURBULENCE

The idea, suggested by Gao Ge in 1985, that KdV-Burgers equation can be regarded asthe normal equation of turbulence is shown to be meaningful by the present paper using thetravelling wave analytic solution of KdV--Burgers equation. By analyzing the cascading downprocess of turbulence, it is pointed out that the process proceeds on a geometrical serieswith a common ratio due to the intermittence of turbulence. The energy spectrum of turbu-lence is obtained from the perturbation velocity solution of KdV--Burgers equation. The slopeof energy--spectrum lies between -- 1.76 and --1.97 in the dilogarithmic coordinate paper. Thecorresponding fractual dimensions lie between 2.09 and 2.72 in terms of intermittencyturbulence model by Frisch (1978). The physical mechanism o? dissipation and dispersioneffects for turbulence is discussed by means of atmospheric dynamics.