The dynamics of spinning detonation waves

The fluid motion of chemically reacting gases in a weak detonation wave is examined with a view to finding a dynamical theory of the spin phenomenon. It is shown that a reacting gas in which the rate of reaction increases with temperature is unstable with respect to wave motion. The amplitude of any wave tends to increase exponentially with time until the growth rate is checked by some dissipative process. Two such processes are examined: first, the drag on a rotating wave at the boundary of the tube, and secondly, the development of weak transverse shocks from the large amplitude acoustic waves in the reaction zone. The formulae obtained are compared with observations and are shown to be not inconsistent with the proposed mechanism of the spinning detonation wave.