The Theoretical Model of Atmospheric Turbulence Spectrum in Surface Layer

It is shown that the slope of energy spectrum obtained from the velocity solution of Kdv-Burgers equation lies between -5/3 and -2 in the dilogarithmic coordinates paper. The spectrum is very close to one of Kolmogorov’s isotropic turbulence and Frisch’s intermittent turbulence in inertial region. In this paper, the Kdv-Burgers equation to describe atmospheric boundary layer turbulence is obtained. In the-equation, the 1 / Re corresponds to dissipative coefficient v, Ri1/2 to dispersive coefficient β, then (v/2β)2 corresponds to 1 /Re2 ·Ri. We prove that the wave number corresponding to maximum energy spectrum S(k) decreases with the decrease of stability (i.e., the increase of (v / 2β)2 in eddy-containing region. And the spectrim amplitude decreases with the increase of (v / 2β)2 (i.e., the decrease of stability). These results are consistent with actual turbulence spectrum of atmospheric surface layer from turbulence data.