Nonlinear hydrodynamic stability and spinning deflagration of liquid propellants

Considered is a dynamic model of liquid propellant combustion that generalizes the classical model due to Landau. In appropriate parameter regimes, this model exhibits the well-known phenomenon of hydrodynamic (Landau) instability, in which steady planar deflagration is unstable to steady, but nonplanar (cellular), modes of combustion. In a cylindrical geometry, there exist special values of the radius such that the basic solution simultaneously loses stability to two cellular modes at critical values of a parameter that determines the sensitivity of the reaction rate to the local pressure field. A nonlinear stability analysis in the neighborhood of certain members of this sequence of double eigenvalues then leads to the prediction, by either one or the other of two methods, of secondary and tertiary branching of orbitally stable, spinning deflagration waves.