不混和微粒子の上昇・沈降に励起される流体運動 : 微粒子を含むマグマの対流  [in Japanese] Fluid Motion Induced by Flotation/Sedimentation of Immiscible Particles : Applications to Magmatic Convection  [in Japanese]

不混和微粒子と粘性流体とが密度差により重力分離する場合に励起される流体運動について理論的に考察した。まず二相からなる混相流体の基礎方程式系を新しく導いた。特に二相の相対運動の効果をあらわに取り入れた。線形安定論の結果, 微粒子が一様に分布する状態は, 微粒子体積分率の無限小振幅擾乱に対して中立安定であることが分かった。そこで有限振幅の微粒子擾乱を与えた場合について2次元非定常非線形数値解析を行い流れの時間変化を示した。無次元数や境界条件の違いが, 流れのパターン選択, 流れの持続性, 非線形性に与える影響について調べた。微粒子対流の一般性を理解した上で, 気泡や結晶などの微粒子を含むマグマ対流へ応用した。マグマと微粒子の分離が素早い場合, マグマ溜まり対流は励起されない。これに対し, 分離が遅い場合にはマグマ溜まり全体が対流したり微粒子を多く含むプリュームが発生し, マグマの鉛直方向への混合が促進される。

In an attempt to understand roles of bubbles or crystals in a magma chamber, I investigated fluid motion induced by flotation/sedimentation of fine immiscible particles. Governing equations for immiscible two-phase flow were derived, which are incorporated into an effect of relative motion between two phases. By using two -dimensional non-linear full equations, I analyzed numerically temporal development of fluid motion induced by finite-amplitude disturbances in concentration of buoyant particles at bottom or within the fluid layer. The resultant flow patterns can be classified into three modes: compensation flow, convection and plume mode. Mode selection is strongly dependent on three parameters; Pseudo-Rayleigh number, relative velocity and horizontal wavelength of the disturbances. The compensation flow appears when particles separate swiftly from the ambient fluid. In contrast, if the relative velocity is low, the convective mode becomes dominant. In this mode, the induced velocity of the ambient fluid increases with decreasing of the relative velocity. It is found that the self-sustained cellular convection took place only in a system with homogeneous production of buoyant particles at the bottom. In case of an extremely lower relative velocity, advected particles tend to make abuoyant layer above the bottom and consequently, a plume rises from the layer through an instability similar to the Rayleigh-Taylor instability. I applied the above results into a magma chamber convection induced by bubble flotation. If the bubble size is below a critical range or the magma is correspondingly more viscous, the induced flow is of the self-sustained convection or plume mode. In this situation, magma at depth will be transferred upward as plume including many vesicles and, therefore, comparatively inhomogeneous magma mixing may proceed. These sustained modes of particle-driven convection may destabilize the magma chamber under a thermally stable condition to trigger an eruption. On the contrary, when the bubble size exceeds the critical size range or the viscosity of magma is correspondingly lower, bubble separate so rapidly from the magma that a whole chamber convection does not occur. Consequently, effective magma mixing would not proceed.