Effect Of Compressibility On The Evolution Of The Rayleigh-Taylor And Richtmyer-Meshkov Instabilites

Interfacial instabilities between different fluids include the Rayleigh-Taylor(RT)instability and the Richtmyer-Meshkov(RM)instability that occur perpendicular to the fluid interface and the Kelvin-Helmholtz(KH)instability that occurs when different layers of the fluid move tangentially.These interfacial instabilities are important for many natural phenomena and industrial processes such as supernova explosion,inertial confinement fusion(ICF),atmospheric motion,etc.In the initial stage of the RT instability,the perturbation amplitude increases exponentially with time.As the perturbation amplitude approaches its wavelength,the nonlinear growth of perturbation begins to occur.Then,the light fluid forms bubbles in the heavy fluid,and the heavy fluid forms spikes in the light fluid.Finally,light and heavy fluids mix with each other and turbulence occurs.The RM instability takes place at the interface that a shock wave passes through,and its evolution process is the same as the RT instability.The description of nonlinear evolution of the RT and RM instabilities has always been debated.In order to describe the nonlinear evolution of bubble,based on the idea of single mode,Layzer and Zufiria put forward the velocity potential and complex potential theories,respectively.The early studies on the nonlinear evolution of RT and RM instabilities mainly focus on ideal fluids regardless of incompressibility,surface tension and viscosity.In recent years,many experimental,theoretical and simulation studies have been carried out on the influence factors of viscosity,surface tension,compressibility,heat diffusion,heat conduction,head loss and so on.For real fluids,the effect of compressibility is inevitable and complex.In previous studies of compression,the part of change in pressure and density caused by interface motion has not been taken into account.In chapter 1,a brief overview of fluid and fluid instability is given.In chapter 2,the basic properties of fluid are introduced.In chapter 3,fluid instability is introduced,including flow instability and interface instability.In chapter 4,the research progress of the RT and RM instabilities are introduced,including the introduction of Layzer-type and Zufiria-type models,as well as the discussion of the influence of surface tension and viscosity on the above two kinds of instabilities.Then,based on Layzer-type and Zufiria-type models,the evolution of bubbles in the RT and RM instabilities of compressible fluids is studied.According to the adiabatic equation,density?and adiabatic exponent?are parameters that reflect compressibility at a given static pressure p.By innovativelyand the time-varying pressure,density and bubble velocity are related together.Then the governing equation of bubble evolution in the RT and RM instabilities of compressible fluids are derived,and the effects of density and adiabatic exponent are analyzed and discussed.For the RT instability,a conclusion is drawn from Layzer-type model:the upper fluid adiabatic exponent?_uand density?_uincrease the bubble amplitude and velocity,but they decrease the bubble curvature radius in the early stage,while the lower fluid adiabatic exponent?_land density?_l have the opposite effects to those of?_uand?_u,consistent with recent results.It is concluded from Zufiria-type model that?_u and?_u promote the development of the RT instability,while the effect of?_l and?_l is opposite to that of?_u and?_u,which is consistent with the conclusion obtained within Layzer-type model.For the RM instability,because density is a function of adiabatic exponent,it is difficult to distinguish the independent effects of these two parameters.whereas,the influences of adiabatic exponent and density are different in the early and late stages of the RM instability,and based on this,we can obtain separately the effects of density and adiabatic exponent:?_uand?_udecrease the bubble amplitude and velocity,but they increase the bubble curvature radius in the early stage,however,the effects of?_l and?_l are opposite to those of?_uand?_u.Moreover,we find a good agreement between our three-dimensional results of the RM bubble amplitude and recent numerical simulations.For the RT and RM instabilities in fluids with high relative velocities or real gases,the influence of compressibility is very important.The presented results provide a valuable guidance for studying the effect of compressibility on ICF,underwater explosion and other practical situations.