of a two-dimensional cellular detonation, after [4], similar to

If we make the assumption of a weakly curved detonation shock, a near-CJ detonation velocity, and a quasi-steady detonation flow, then it is possible to derive an equation(s) for the evolution of the smooth part of the shock surface in space and time. The asymptotic derivation specifically relates the normal detonation velocity, Dn, to the local shock curvature, K. The functional relationship between Dn and K depends on the detailed equation of state and the rate law. This work, with John Bdzil of Los Alamos National Laboratory, is completely described in a series of papers [1, 9, 8, 2, 3, 7].