Reviewer #1: 1. We added a definition of LSB in the abstract before using it. 2. It is unclear how to address the reviewer's comment, which suggests that "Perhaps some of the these elements can be eliminated without losing focus on the key contribution." Although the work is the second in a two-part report, we tried to ensure that each would stand alone as an independent publication. Repetition is unavoidable. Reviewer #2: 1. We added a reference for the chemical/transport/thermodynamics model used, and included a justification of the transport approximation. 2. The grid resolution we used for this study is indeed sufficient, as shown in a reference we now cite. 3. The upstream shift in the experimantal flame location for U_0 = 10 m/s is shown on the axial profiles in Fig. 3a. The magnitude of the shift is small (about 3 mm) and is not readily discernable on the vector plots. We revised the manuscript to point this out in Fig 3a. We also added the simulated profiles to Fig. 3a to aid in the discussion. The q'/U_0 profiles for the simulations are not shown because of the large uncertainties associated with the azimuthal averaging used -- near the symmetry axis, azimuthal averaging does little to improve the statistics of the mean diagnostics. As discussed, and referenced, in the text, the global features of these flames can be well-simulated if the fidelity of the inflow is increased considerably. The primary focus of this paper however is the detailed structure of the flame rather than accurately capturing the large-scale flame dynamics. In this context, flame brush statistics are used primarily to ensure that the simulation is capturing the correct regime of turbulent-flame interaction. 4. The reviewer has a valid point that our choice of flame progress could seem inconsistent. We added text to highlight the issues peculiar to this flame, and to justify the use of the temperature field for computing curvature and the fuel concentration for progress through the reaction zone. 5. Slight broadening of the reaction front is seen for the very weak burning groups at s > 0. This qualification is added to the narrative. 6. We included an equation for dH2, based on the expressions we added for the transport approximation. 7. There has been some recent work to relate the local properties of cellular lean hydrogen-air flames to a collection of 1D unstrained steady flame profiles, including some of our own work. Moreover, there has been some effort to build flamelet-based models on these and other observations (to steady strained flames, for example). Although that body of research shows promise as a route to efficient modeling of such flames, it is only tangentially related to our investigation here. We do not see any benefit to adding a family of curves to many of the plots in this paper, since none of the analysis or discussion is directly related to flamelet models. 8. We added text to the paper to clarify that the Lagrangian analysis frame is the more correct viewpoint to use when trying to understand these complex flows. Eulerian paths are only approximately correct, to the extent that the conditions remain statistically similar as a parcel of fluid moves from the cold region upstream and through the reaction zone. Minor comments: 1. We fixed all incidences of "et al" to "et al." 2. We fixed the equation for the local atomic stoichiometry. 3. Fig. 7b replotted using the parameters discussed above. 4. We thank the reviewer for pointing out the lack of convergence of the local stoichiometry to the 1D line for c < 0.2. It was caused by an error in our algorithm that failed to account for the fact that the Lagrangian statistics start at different c values for each pathline followed. The algorithm has been corrected and the new Fig. 10 shows the the expected convergence. 5. We fixed the caption to Fig 18. Reviewer #3 1. We added a number of references to the body of literature on flames of this type by other authors. [todo: MSD] 2. The paper already included a review of simulation work that successfully captured the large-scale stabilization of these types of flames, but we added new text to this paper to emphasize that the current sutdy is focused on local turbulence-chemistry interactions. 3. The Kolmogorov length scales in these flames are greater than 100 microns. The low Mach number simulations used here fully resolve the turbulence and flame structures, as referenced. In that sense, this is a "DNS", and the discription of the model and solution method is complete as is. We added a reference to a detailed analysis of the mesh resolution requirements for this flame. We also added a more detailed description of the outflow boundary conditions, as requested by the reviewer. 4. Case H-E is useful to discuss in the context of the experimental data, even if it was not simulated. It is clear throughout the paper that only two cases were simulated. We added a forward reference to the two additional quantities in the Table that are discussed in a subsequent section. In our opinion this is superior to adding a separate small table for these quantities later. 5. We also added the simulated profiles to Fig. 3a to for a direct comparison between experiments and simulations.The q'/U_0 profiles from the simualtions are not shown (as discussed in our response to Reviewer #2's third point). 6. We disagree that showing yet another picture of computed cellular flame structures would be useful here. There are many examples in the cited literature of such images. 7. The procedue to deduce a_z and z_0 are described in Cheng et. a. POCI 2009. We added this citation. 8. We thickened the flame isotherms in Fig. 4 & 5 to improve readibility. 9. We modified the text to indicate that the cellular patterns observed in the data are the result of an interaction of the turbulence with the thermodiffusive transport properties of the flame. 10. The reviewer misquoted the manuscript text. We make no statement about relationship of either of these to strain. It is unclear how we should respond. 11. We fixed the caption for figure 9. 12. The JPDF of integrated fuel consumption and max fuel consumption rate is the key to defining the five different burning groups. This allows us to use the criteria of Table 1 to extract pathlines for each group in a consistent manner. 13. The reviewer failed to understand that the plot shows statistical quantities. The regions with extreme values of fuel consumption have extremely low (but nonzero) probability. 14. We do not understand the reviewer's concern. By the nature of its definition, the quantity, Sc/Sl, implies some enhancement of consumption on a flame surface due to turbulence. The integrated fuel consumption is a more direct measure of burning enhancement; it avoids the abiguity of associating consumption with an ill-defined surface. 15. We removed the speculation/expectations regarding atomic stoichiometry. The reviewer is correct that this didn't demonstrate anything of substance. 16. We defined the divergence of the diffusive flux divergence. 17. ?? 18. It is unclear how to 'mathematically demonstrate' Lagrangian pathlines. It is self-evident that the Lagrangian diagnostic is a time history of a parcel of fluid. We don't understand how to better clarify this definition. 19. We are not attempting to improving the conventional edge filter method for extracting reaction fronts from OH-PLIF. The objective of the new method is the use of an additional parameter, i.e. |grad(OH)|- as a condition to remove nonphysical edges which would otherwise appear on the backside of the flame. This is explained on page 12 second paragraph. The ultimate goal is to have a consistent way to analyze OH-PLIF images obtained from non-broken flame edges (i.e. CH4) and broken flame edges (i.e. CH4/H2 blend and H2). As a necessary verification step, we applied the |grad(OH)| method to the CH4 flame data reported in Ref [1] and confirmed the validity of this approach to non-broken flames. We are not using a value of |grad[OH]| from the pathline for conditioning. The pathline OH data are used to support the physical argument that the reacting fronts are characterized by steep |grad[OH]|. In fact, what we have done exactly what this reviewer indicated in the last sentence of this comment i.e. "a simple threshold on OH and gradient of OH (not on the pathline)" Reviewer #4 1. The pathline diagnostic is initiated from a uniform distribution of points above the nozzle on the 350K isotherm. As they move downstream, they become nonuniformly distributed through the reaction zone. In fact, as discussed in the paper many of the paths never actually experience significant combustion reactions. As a result, the diagnostic suggested by the reviewer would require a number of arbitrary definitions, and is thus likely to generate considerable controversy, rather than elucidating something about the flame statistics. 2. Although it is well-known that the thermodiffusive instability in low Lewis number flames leads to cellular flame patterns, we acknowledge that in our study, the patterns are modulated by turbulence. We modified the text throughout the paper to avoid attributing the cellular patterns entirely to the instability of the turbulence alone. 3. See Reviewer #3 item 19 answer 4. We fixed the text to refer only to the experimental data (since simulation data was not used, and served no purpsoe, in this figure).