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We propose a mechanism to produce fluctuations in the viscosity parameter($\alpha$) in differetially rotating discs. We carried out a nonlinear analysisof a general accretion flow, where any perturbation on the background $\alpha$was treated as a passive/slave variable in the sense of dynamical systemtheory. We demonstrate a complete physical picture of growth, saturation andfinal degradation of the perturbation as a result of the nonlinear nature ofcoupled system of equations. The strong dependence of this fluctuation on theradial location in the accretion disc and the base angular momentumdistribution is demonstrated. The growth of fluctuations is shown to have atime scale comparable to the radial drift time and hence the physicalsignificance is discussed. The fluctuation is found to be a power law in timein the growing phase and we briefly discuss its statistical significance.

Time variability of viscosity parameter in differentially rotating discs