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In this work the limitation of using a frozen model to describe a turbulent medium is discussed. Among other assumptions, the frozen model requires the statistically independent velocity fluctuations to have infinitely large scales in comparison with scales of the refractive index fluctuations. When the scale of velocity fluctuations becomes comparable with or smaller than the scale of refractive index fluctuations, the frozen model is no longer valid and has to be modified. Upon three hypotheses, a non-frozen model is proposed in this paper. These hypotheses are generalizations of the ones used in the past. They include: (1) Both the refractive index and the velocity field of the turbulence are isotropic, stationary, homogeneous, and jointly stationary and homogeneous with each other. (2) The medium is incompressible. (3) The refractive index is conservative. Based on this non-frozen model several formulas for the space-time autocorrelation function and the wave-number frequency spectrum of the refractive index are derived. Electromagnetic wave scattering from a turbulent medium characterized by this non-frozen model is studied. The width of frequency spectrum and the mean frequency shift have been obtained. The results show that the power spectrum of the scattered field can no longer be regarded as equal to the velocity spectrum of the turbulence in general. The modification is important especially when the scale of velocity fluctuations is small in comparison with the electromagnetic wavelength. In Appendix the effects of finite radar pulse volume and radar beam broadening on the width of frequency spectrum of radar echos from a non-frozen turbulence drifting perpendicularly to the axis of the radar beam are investigated.