The expansion of a wedge of gas into a vacuum

Abstract

AbstractThe front from the expansion into a vacuum of an infinite wedge of polytropic gas initially at rest at constant pressure is studied in detail. It is shown how the shape of that part of the gas-vacuum interface resulting from the presence of the sharp corner changes with the wedge angle and the adiabatic index of the gas. In addition to analytic results for wedges of arbitrary angle, numerical results substantiating the analysis are given for the special case of 90°. Finally, explicit formulae for the path of a particle initially part of a 60° wedge of water allowed to collapse at time t = 0 are derived from an exact linear solution obtained by Suchkov and interpreted through the hydraulic analogy for adiabatic index 2.