| Abstract: | The stability of steady-state flow is considered in a medium with a nonlocal coupling between pressure and density. The equations for perturbations in such a medium are derived in the linear approximation. The results of numerical integration are given for shear motion. The stability of parallel layered flow in an inviscid homogeneous fluid has been studied for a hundred years. The mathematics for investigating an inviscid instability has been developed, and it has been given a physical interpretation. The first important results in flow stability of an incompressible fluid were obtained in the papers of Helmholtz, Rayleigh, and Kelvin 1] in the last century. Heisenberg 2] worked on this problem in the 1920's, and a series of interesting papers by Tollmien 3] appeared subsequently. Apparently one of the first problems in the stability of a compressible fluid was solved by Landau 4]. The first investigations on the boundary-layer stability of an ideal gas were carried out by Lees and Lin 5], and Dunn and Lin 6]. Mention should be made of a series of papers which have appeared quite recently 7–9]. In all the papers mentioned flow stability is investigated in the framework of classical single-phase hydrodynamics. Meanwhile, in recent years, the processes by which perturbations propagate in media with relaxation have been intensively studied 10–12].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 87–93, May–June, 1976. |
