Nonlinear Development of Low Frequency One-Dimensional Instabilities for Reacting Shock Waves

The classical theory of von Neumann, Zeldovich, and Doering (the ZND theory) from the early 1940’s postulates that detonation waves are steady traveling waves with a quasi one-dimensional structure of an ordinary fluid dynamic shock followed by a reaction zone. In contrast, the detonations observed in many experimental circumstances demonstrate extremely complicated unstable wave patterns (see Oppenheim & Soloukhin [1], Fickett & Davis [2], Lee & Moen [3]). The nature of these instabilities ranges from complex transverse Mach stems in gases to regular and chaotically irregular pulsating fronts in both gaseous and condensed phases. Understanding the mechanisms responsible for the correspondingly higher pressures in unstable detonations has obvious practical implications.