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In this article, we investigate the energy cascade of three-dimensional turbulent flows, in which the breakdown process of eddy is quasi-self similar.Mathematically this kind of turbulence with quasi-self similar structure eddies can be regarded as cookie-cutter system [1], and could be generated by self-similar iterated function system (IFS) by adding nonlinear disturbance.The cookie-cutter system obeys the principle of bounded aberrance [2].This fact makes it possible to define Gibbs measure to get Hausdorff dimension of its attractor of this kind system [3].