Abstract
This chapter begins with a discussion of buoyancy as a driving force and proceeds to derive the dispersion relation for the Rayleigh-Taylor instability. It considers Rayleigh-Taylor in several specific contexts, the generalization of Rayleigh Taylor, sometimes called the entropy mode , and the nonlinear behavior of Rayleigh-Taylor-unstable systems. It hen discusses lift as a driving force, proceeds to derive the dispersion relation for the Kelvin-Helmholtz instability, and discusses Kelvin-Helmholtz in several specific contexts. Following that, it discusses the stability of shock waves and then the Richtmyer-Meshkov process, through which deposition of vorticity leads to evolving structure. The chapter concludes with a discussion of hydrodynamic turbulence.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bychkov VV, Liberman MA, Velikovich AL (1990) Analytic solutions for Rayleigh-Taylor growth-rates in smooth density gradients – comment. Phys Rev A 42(8):5031–5032
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic stability. Dover, New York
Dimonte G (2000) Spanwise homogeneous buoyancy-drag model for Rayleigh-Taylor mixing and experimental evaluation. Phys Plasmas 7(6):2255–2269
Dimotakis PE (2000) The mixing transition in turbulent flows. J Fluid Mech 409:69–98
Dimotakis PE (2005) Turbulent mixing. Annu Rev Fluid Mech 37:329–356
Duff RE, Harlow FH, Hirt CW (1962) Effects of diffusion on interface instability between gases. Phys Fluids 5(4):417–425. https://doi.org/10.1063/1.1706634
Haan SW (1991) Weakly nonlinear hydrodynamic instabilities in inertial fusion. Phys Fluids B-Plasma Phys 3(8):2349–2355. https://doi.org/10.1063/1.859603
Hinze JO (1959) Turbulence. McGraw-Hill, New York
Ishizaki R, Nishihara K, Sakagami H, Ueshima Y (1996) Instability of a contact surface driven by a nonuniform shock wave. Phys Rev E 53:R5592–R5595
Jackson JD (1999) Classical electrodynamics. Wiley, New York
Landau LD, Lifshitz EM (1987) Fluid mechanics, course in theoretical physics, vol 6, 2nd edn. Pergamon, Oxford
Oron D, Arazi L, Kartoon D, Rikanati A, Alon U, Shvarts D (2001) Dimensionality dependence of the Rayleigh-Taylor and Richtmyer–Meshkov instability late-time scaling laws. Phys Plasmas 8(6):2883–2890
Richtmyer RD (1960) Taylor instability in shock acceleration of compressible fluids. Commun Pure Appl Math 13:297
Tennekes H, Lumley JL (1972) A first course in turbulence. MIT Press, Cambridge
Tritton DJ (1988) Physical fluid dynamics, 2nd edn. Clarendon Press, Oxford
Velikovich AL (1996) Analytic theory of Richtmyer–Meshkov instability for the case of reflected rarefaction wave. Phys Fluids 8(6):1666–1679
Velikovich A, Phillips L (1996) Instability of a plane centered rarefaction wave. Phys Fluids 8(4):1107–1118
Wouchuk JG, Cobos-Campos F (2017) Linear theory of Richtmyer–Meshkov like flows. Plasma Phys Control Fusion 59(1). https://doi.org/10.1088/0741-3335/59/1/014033
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Drake, R.P. (2018). Hydrodynamic Instabilities. In: High-Energy-Density Physics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-67711-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-67711-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-67710-1
Online ISBN: 978-3-319-67711-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)