Huygens' Principle geometric derivation and elimination of the wake and backward wave

Abstract

Huygens' Principle (1678) implies that every point on a wave front serves as a source of secondary wavelets, and the new wave front is the tangential surface to all the secondary wavelets. But two problems arise: portions of wavelets that exist outside of the new wave front combine to form a wake. Also there are two tangential surfaces so wave fronts are propagated in both the forward and backward directions. These problems have not previously been resolved by using a geometrical theory with impulsive wavelets that are in harmony with Huygens' geometrical description. Doing so would provide deeper understanding of and greater intuition into wave propagation, in addition to providing a new model for wave propagation analysis. The interpretation, developed here, of Huygens' geometrical construction shows Huygens' Principle to be correct: as for the wake, the Huygens' wavelets disappear when combined except where they contact their common tangent surfaces, the new propagating wave fronts. As for the backward wave, a source propagates both a forward wave and a backward wave when it is stationary, but it propagates only the forward wave front when it is advancing with a speed equal to the propagation speed of the wave fronts.

Crankcase Explosions in Marine Diesel Engines: A Computational Study of Unvented and Vented Explosions of Lubricating Oil Mist

“…The stages of flame ignition, propagation, and acceleration in the oil mist were simulated using the FT model based on the Huygens principle stating that each point on the flame front is itself the source of spherical wavelets, whereas the secondary wavelets emanating from different points mutually interfere [89]. Within the FT model, the flame is an infinitely thin surface separating the fresh mixture from combustion products and is traced explicitly at the subgrid level.…”