Uritsky, Davila, and Jones Reply: Systems in the state of self-organized criticality (SOC) are known to exhibit power-law distributions of energy dissipation events con- ventionally called avalanches. Finding this type of statis- tical behavior in experimental data or simulation outputs cannot itself constitute a rigorous proof of SOC (to obtain such a proof, one needs to evaluate a comprehensive set of critical exponents, perform the finite-size scaling analysis, and verify scaling relations predicted for the universality class of interest). However, the power-law form of heavy- tailed avalanche distributions is commonly considered as a necessary condition for a system to be a candidate for SOC dynamics. Using the data kindly provided by Watkins, Chapman, and Rosenberg in the preceding Comment [1], we have found that the complementary cumulative distribution function (CDF) of the burst size s reported in their Figure 2 is not a power-law distribution. Our Fig. 1 shows that the log-normal CDF defined as PðsÞ¼ 1=2½1  erf ððlns  Þ= ffiffiffi 2 p Þ provides a reasonable fit to the tail portion (s> 1) of this distribution. It also demonstrates that the burst size statistics of the p model does not have a well-defined range of energy scales that could be approxi- mated by a local power-law fit. As can be seen from the inset plot, the local log-log slope of the distribution under- goes a systematic change across the entire range of scales studied. This change is consistent with the log-normal fit but not with a power-law fit whose local slope stays at a constant level. Therefore, the model discussed in the Comment cannot be used as an example of a turbulent system exhibiting SOC. Having said that, we would like to express our agree- ment with the main idea of the Comment that fluid turbu- lence can, in principle, display signatures of SOC. This possibility has been tested in a number of previous simu- lation studies [2–4], and it has been explored in detail in our recent work [5]. The results obtained so far suggest that in order for a high-Reynolds number fluid to reach the state of SOC, the fluid dynamics should include two distinct modes of energy transport with well-separated time scales (by analogy with stick-slip or depinning transitions of SOC models). In a resistive magnetized fluid such as the plasma of the solar corona, this condition can be fulfilled through convective and diffusive mechanisms of magnetic energy transport [5]. The results presented in the Comment make us believe that simplified statistical models of turbulent cascade are unable to reproduce such behavior. Our final comment is on the nature of power-law dis- tributions in the bursty coronal dissipation associated with the flaring activity. The coronal velocity field as measured by nonthermal spectral line broadening shows a surpris- ingly low level of turbulence [6]. This fact suggests that the coronal complexity described in [7] is driven by an un- stable magnetic field topology rather than by classical fluid cascades in the k space. Certain aspects of this process are captured by discrete avalanching models ([8,9] and refer- ences therein), but its first-principle description is still to be found. Vadim M. Uritsky, 1 Joseph M. Davila, 2 and Shaela I. Jones 3 1 University of Calgary Calgary, AB T2N1N4 Canada 2 Goddard Space Flight Center Greenbelt, Maryland 20771, USA 3 University of Maryland College Park, Maryland 20742, USA Received 5 February 2009; published 16 July 2009 DOI: 10.1103/PhysRevLett.103.039502 PACS numbers: 96.60.P , 05.65.+b, 52.35.Ra [1] N. W. Watkins, S. C. Chapman, and S. Rosenberg, preced- ing Comment, Phys. Rev. Lett. 103, 039501 (2009). [2] F. Reale et al., Astrophys. J. 633, 489 (2005). [3] S. Galtier and A. Pouquet, Sol. Phys. 179, 141 (1998). [4] P. Dmitruk and D.O. Gomez, Astrophys. J. 484, L83 (1997). [5] A. J. Klimas et al., arXiv:astro-ph/0701486v3. [6] J. L. R. Saba and K. T. Strong, Astrophys. J. 375, 789 (1991). [7] V.M. Uritsky et al., Phys. Rev. Lett. 99, 025001(2007). [8] P. Charbonneau et al., Sol. Phys. 203, 321 (2001). [9] D. Hughes et al., Phys. Rev. Lett. 90, 131101 (2003). FIG. 1 (color online). Main panel: Complementary CDF of burst sizes of the p model (solid line) and its suggested log- normal fit ( ¼1:69,  ¼ 3:49). Inset: Local log-log slopes (one slope per decade) of the two distributions; error bars indicate  2 standard deviations from average slopes. The dotted horizontal line shows the slope 0:44 corresponding to the burst size exponent 1.44 reported in the Comment by Watkins et al.. Note that this slope value is not associated with any plateau in the inset plot, making it clear that the proposed power-law fit is not justified. This excludes the possibility that the p model exhibits SOC, contrary to the main claim of the Comment. PRL 103, 039502 (2009) PHYSICAL REVIEW LETTERS week ending 17 JULY 2009 0031-9007= 09=103(3)=039502(1) 039502-1 Ó 2009 The American Physical Society