Abstract
A previous calculation [P. H. Diamond and T.-S. Hahm, Phys. Plasmas 2, 3640 (1995)] of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence ∼kmin−3, is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on kmin. The original divergence is traced to an inconsistent resonance-broadening type of diffusive approximation, which fails in the present problem. Ballistic scaling of renormalized pulses is retained, but such scaling does not, by itself, imply a paradigm of self-organized criticality. An improved scaling formula for a model with velocity shear is also given.
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