Hydrodynamic Instabilities and Turbulence Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz Mixing
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Part 1 Fundamentals
- 1 A first glimpse of Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities
- 2 The linear stage for a singlemode
- 3 The nonlinear stage for a singlemode
- 4 Multimode instabilities: Linear and nonlinear regimes
- 5 Global features from the lens of integrated mixingmeasurements
- 6 Internal dynamics from the lens of statistical mixingmeasurements
- 7 Elementary aspects of turbulent flows
- 8 Transition to turbulence
- Part 2 Hydrodynamics of Complex Flows
- Part 3 From the Microscopic to Cosmic Scales
- References
- Index
2 - The linear stage for a singlemode
from Part 1 - Fundamentals
Published online by Cambridge University Press: 27 June 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Part 1 Fundamentals
- 1 A first glimpse of Rayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz instabilities
- 2 The linear stage for a singlemode
- 3 The nonlinear stage for a singlemode
- 4 Multimode instabilities: Linear and nonlinear regimes
- 5 Global features from the lens of integrated mixingmeasurements
- 6 Internal dynamics from the lens of statistical mixingmeasurements
- 7 Elementary aspects of turbulent flows
- 8 Transition to turbulence
- Part 2 Hydrodynamics of Complex Flows
- Part 3 From the Microscopic to Cosmic Scales
- References
- Index
Summary
In this chapter, we focus on some simple cases in which analytical treatments of the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities can be carried out. This requires neglecting many physical effects and assuming small amplitude perturbations of a single wavelength. The linear stage growth rates are loosely derived and explored. This treatment requires the introduction of the key fluid equations and the concepts of vorticity, species fractions, and diffusion. Comparison is made to experiments.
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- Hydrodynamic Instabilities and TurbulenceRayleigh–Taylor, Richtmyer–Meshkov, and Kelvin–Helmholtz Mixing, pp. 16 - 38Publisher: Cambridge University PressPrint publication year: 2024
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