Multifront Wave Research Articles

Solitary wave and multi-front wave collisions for the Bogoyavlenskii–Kadomtsev–Petviashili equation in physics, biology and electrical networks

In this paper, we investigate a Bogoyavlenskii–Kadomtsev–Petviashili equation, which can be used to describe the propagation of nonlinear waves in physics, biology and electrical networks. We find that the equation is Painlevé integrable. With symbolic computation, Hirota bilinear forms, solitary waves and multi-front waves are derived. Elastic collisions between/among the two and three solitary waves are graphically discussed, where the waves maintain their shapes, amplitudes and velocities after the collision only with some phase shifts. Inelastic collisions among the multi-front waves are discussed, where the front waves coalesce into one larger front wave in their collision region.

Multi-front waves for extended form of modified Kadomtsev-Petviashvili equation

An extended form of the modified Kadomtsev-Petviashvili (mKP) equation is investigated. The simplified form of the Hirota bilinear method established by Hereman and Nuseir is employed. Multi-front wave solutions are formally derived to the extended mKP equation and the mKP equation. The results show that the extension terms do not kill the integrability of the mKP equation.

Characteristic regimes of multifront-detonation propagation along a convex surface

Experimental results of multifront-detonation diffraction on a convex curvilinear surface are given. An estimate of the minimum gas-layer thickness, which is necessary for the external circumferential rotation of a multifront wave, is proposed. The characteristic propagation regimes are established in annular channels: complete destruction of detonation and combustion, high-speed combustion, galloping detonation, and multifront detonation.

Critical conditions for initiation of cylindrical multifront detonation

A quantitative relation between the characteristic scales determining the excitation and propagation of cylindrical and spherical detonation waves is found with the use of a technique for diffraction reinitiation of multifront detonation. The effect of the channel depth on the reinitiation conditions is studied. The ideal character (the smallness of losses) of a cylindrical multifront wave is estimated, and this estimate is found to be in agreement with experimental data.

Nonstationary phenomena in gaseous detonation

Recent progress in the shock-tube study of ignition kinetics in various detonable gases can be now utilized for the interpretation of gasdynamic phenomena associated with the detonation process. As a consequence of current knowledge of these processes, globally stationary multiwave detonations must be considered as intimately associated with such essentially nonstationary flow phenomena as those occurring in the course of the transition to detonation or in the decoupling and re-establishment of the detonation wave that takes place close to the limits of detonability. In particular, the following features have come to light: 1. Ignition kinetics associated with the transition to detonation should be considered under the transient gasdynamic processes, and this must include, the effects of positive temperature and density gradients in the flow field. While the induction time can be “accumulated” in a simple compression wave, in a shock-heated gas an “explosion in explosion” may develop leading to the establishment of a detonation wave. More detailed gasdynamic analysis based on concrete kinetics may explain the difference in the length of “induction distances” observed in various experiments. Similar type of phenomena can be observed when the detonation wave is initiated by incident or reflected waves in shock tubes. 2. Blast waves or diffracting detonation waves in a combustible mixture produce negative gradients in the temperature and density behind the shock front. Even in quite strong waves, with parameters close to the CJ condition, the ignition zone becomes decoupled from the shock front and a local, secondary self-ignition may occur in the shock-compressed gas, leading to the re-establishment of detonation. The multilocus ignition mechanism observed in shock-tube experiments can be used to explain some of these observations. On the basis of ignition kinetics in the transient flow field of a diverging shock front, as it occurs in a decoupled wave, the following estimate of the wave thickness can be derived: τ (ind)≅ (d/dr)τ(ρ, T)rτ (ind), where r is the characteristic thickness of the reaction zone behind the diverging shock front. According to this estimate, the spacing of the wave (i.e., the shock wave radius) should be of the order of 10 r , depending on the value of the activation energy in the rate-controlling reaction. 3. Gasdynamic processes that take place in a multihead detonation front are then explained in relation to both the topics described above. Transverse wave collisions lead periodically to fast explosions of small samples of the compressed gas in the reaction zone, producing a number of nonstationary expanding blast waves. Decoupling processes in these waves can be described in the same terms as those used for divering waves, and an average spacing of transverse waves in a stationary multifront wave can be evaluated. Depending on kinetic parameters of the ignition reactions, a “hydrodynamic” thickness of the multiheaded front may be of about 1 order of magnitude larger than the thickness of a reasonable induction reaction zone in a planar one-dimensional detonation wave. On this basis, recent results of different research groups concerned with the study of the detonation wave structure are discussed.