Weakly Nonlinear Detonation Waves

The authors develop a simplified asymptotic model for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In this regime the fluid mechanical and chemical phenomena interact substantially with each other. The model provides simplified equations for describing this interaction. When the model is specialized to unidirectional combustion waves advancing into a region of uniform flow, the travelling waves of this model system moving with positive speed coincide with the travelling waves in a qualitative model for such effects introduced previously by the second author. Some interesting new combustion waves with partial burning are also analyzed. The two main assumptions in deriving the asymptotic model are weak nonlinearity and a sufficiently high activation energy for the chemical kinetics.