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We reconsider the scenario in which the knee in the cosmic ray spectrum isexplained as due to a change in the escape mechanism of cosmic rays from theGalaxy from one dominated by transverse diffusion to one dominated by drifts.We solve the diffusion equations adopting realistic galactic field models andusing diffusion coefficients appropriate for strong turbulence (with aKolmogorov spectrum of fluctuations) and consistent with the assumed magneticfields. We show that properly taking into account these effects leads to anatural explanation of the knee in the spectrum, and a transition towards aheavier composition above the knee is predicted.Comment: 17 pp., 6 figures; revised version with minor changes. To appear in  JHE

Turbulent diffusion and drift in galactic magnetic fields and the explanation of the knee in the cosmic ray spectrum