Linear stability of plane Poiseuille flow in an infinite elastic medium and volcanic tremors

• Published in: Earth, planets, and space planets, and space, 2014-04, Vol.66 (1), p.1-24, Article 19
• Main Authors: Sakuraba, Ataru, Yamauchi, Hatsuki
• Format: Article
• Language: English
• Subjects: Earth and Environmental Science; Earth Sciences; Fluid flow; Geology; Geophysics/Geodesy; Instability; Laminar flow; Mathematical analysis; Nonuniform; Stability; Symmetry; Tremors
• ISSN: 1880-5981; 1880-5981
• DOI: 10.1186/1880-5981-66-19

The linear stability of a plane compressible laminar (Poiseuille) flow sandwiched between two semi-infinite elastic media was investigated with the aim of explaining the excitation of volcanic tremors. Our results show that there are several regimes of instability, and the nature of stability significantly depends on the symmetry of oscillatory fluid and solid motion. It has been shown that long-wave symmetric instability occurs at a very small value of the Reynolds number, but it is unlikely that this is the cause of volcanic tremors. We show that antisymmetric (flexural) instability also occurs, involving two parallel Rayleigh waves traveling against the Poiseuille flow, but the critical flow speed is faster than that of symmetric instability. However, if the basic flow profile is nonparabolic because of a nonuniform driving force or nonuniform viscosity, the critical flow speed of antisymmetric instability can be considerably slower than that of symmetric instability. Based on numerical calculations and analytical consideration, we conclude that this anomalous antisymmetric instability is possibly produced by a basaltic magma flow of a few meters per second through a dike with thickness of 1 m and extending for several kilometers; this origin can explain some of the characteristics of volcanic tremors.