Mean maganetic field in renovating random flow

An integral equation is derived for a mean magnetic field in a random velocity field that renovates after a characteristic time τ. It is shown that in two cases, i.e. when (1) the correlation time is short, τ very low l/v₀ (where l and v₀ are the characteristic scale and velocity), and (2) for long wave components of the field, k^-1 very large v₀τ, the equation is reduced to the differential one, whose form has first been given by Steenbeck, Krause and Rädler. Expressions for the equation coefficients are obtained in the two above cases. In a general case the integral equation cannot be reduced to the differential one although its spectral properties are close in a certain sense to those of the SKR-equation. There are differences, however, that are shown on the example of the Gaussian distribution of particles moving along random paths.