PPPL-3422 is available in <a href="PPPL-3422.pdf">pdf</a> or 
<a href="PPPL-3422.ps">postscript</a> formats.

<p>
<b>Renormalized Dissipation in the Nonconservatively Forced Burgers Equation</b> </p>

<p>Author: John A. Krommes</p>

<p>
<b>Date of PPPL Report:</b> January 2000
</p>

<p>
<b>Submitted to:</b> Plasmas of Physics</p>

<p>
A previous calculation of the renormalized dissipation in the nonconservatively forced one-dimensional Burgers equation, which encountered a catastrophic long-wavelength divergence approximately [k<sub>min</sub>]<sup>-3</sup> , is reconsidered. In the absence of velocity shear, analysis of the eddy-damped quasi-normal Markovian closure predicts only a benign logarithmic dependence on k<sub>min</sub>. 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.

</p>