PPPL-3422 is available in pdf or postscript formats.

Renormalized Dissipation in the Nonconservatively Forced Burgers Equation

Author: John A. Krommes

Date of PPPL Report: January 2000

Submitted to: Plasmas of Physics

A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [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.