Stability of an interface of velocity discontinuity in a compressible fluid by approach of topological vorticity dynamics

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03672
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Kyushu University
• Principal Investigator: Fukumoto Yasuhide 九州大学, マス・フォア・インダストリ研究所, 教授 (30192727)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: ケルヴィン・ヘルムホルツ不安定性 / 圧縮性流体 / 接線速度不連続面 / 浅水流 / 重力波 / 剪断層 / 表面張力 / 重力

Outline of Final Research Achievements

For an incompressible fluid, a surface of tangential velocity discontinuity necessarily goes through the Kelvin-Helmholtz instability (KHI), by which wavy deformation develops. The growth rate is proportional to the tangential-velocity difference. Compressibility acts to weaken the KHI, and when the Mach number of the tangential velocity difference exceeds √8, the KHI subsides down. The effects of the gravity and surface tension on the KHI of a compressible gas are investigated. When the upper fluid is lighter, gravity acts as a stabilizing force, but both gravity and surface tension cause the KHI which otherwise is stabilized by compressibility effect. There is a mathematical analogy between compressible flows and incompressible shallow water flows. For the latter, gravity waves correspond to sound waves. New instabilities are found for the effect of depth differences and for a shear flow of finite width.

Free Research Field

流体力学

Academic Significance and Societal Importance of the Research Achievements

速度不連続面のKelvin-Helmholtz不安定性（KHI）や重い液体層が軽い層上に乗っているとき、界面が一方的に変形して重い液体が沈み込むのがRayleigh-Taylor不安定性（RTI）で、RTI/KHIは乱流に発達し、界面を隔てた物質の混合を促進する。界面乱流は超新星爆発や太陽フレアなどの天体現象から、レーザー核融合、ナノ材料加工まで幅広く関与するが、一様等方性乱流ほど理解が深まっていない。圧縮性がRT乱流に及ぼす影響は未踏領域である。本研究では、圧縮性によって安定化するKHIを、復元力であるはずの重力と表面張力がむしろ不安定化するという謎めいた結果を得て、新たな課題を提供する。