Deflagration-to-detonation transition (DDT) may occur through the Zel＇dovich or shock wave amplification by coherent energy release (SWACER) gradient mechanism when spatial nonuniformities in temperature and composition are formed through turbulent mixing of reaction products with unburned gas. If the gradient region is large enough, a spontaneous reaction wave will form and strengthen into a detonation that may propagate into the unburned mixture. Such gradient regions formed by turbulent mixing are likely to be highly irregular, containing disturbances with a wide range of magnitudes and length scales. One-dimensional calculations in which a sinusoidal disturbance is superimposed on a linear gradient are used to examine the effect of disturbance amplitude and frequency on the size of a mixed region necessary for DDT. The results suggest that disturbances caused by turbulent mixing may increase the critical length by more than order of magnitude as compared to an undisturbed linear gradient. Disturbances of intermediate frequency increase the critical length more than those of very low or very high frequency. Large-amplitude disturbances increase the critical length by effectively dividing the gradient into subregions.