Interface Physical Continuous Distribution Of Rayleigh - Taylor Instability

Hydrodynamic instability is an important issue on the engineering of Inertial Confinement Fusion, especially the Rayleigh-Taylor instability, is a vital problem during the ICF capsule implosions and the central hot spot ignitions. Efforts are focused on this subject in many related laboratories though Simulations, theoretical and experimental studies. As in theories, many useful formulas and conclusions had obtained from classical potential flow model, or sharp boundary model, including nonlinear results of interfacial and bubble evolution. But in real problems observed by simulations and experiments, for perturbations of short wavelength, the sharp boundary is necessary to be modified to continual profile of quantities such as density, pressure and so on.Earlier work on hydrodynamic instability of continual steady state based on linearization of Navier-Stokes equation, boundary value problem obtained such as Orr-Sommerfeld equation. Fruitful contents of linearization of Magnetohydrodynamic equations had been summarized by Chandrasekhar; one of the eigenvalue problems in his book can be regarded as a standard form of RTI for incompressible fluids, noticed by Mikaelian and proved by Kull. Then Vandervoort, who changed the incompressible condition to be conservation of specific entropy for ideal flow, got immediately an eigenvalue problem for compressible fluids. In the PhD dissertation of Fan Zhengfeng, a third-order perturbation equation from linearization about steady ablation had been solved numerically and many interesting results had been waiting for comprehension.This work provides some understandings based on eigenvalue problems of linear RTI, including density-gradient effect on incompressible RTI and Kelvin-Helmholtz instability, and compressibility effect on RTI, some approximate growth-rate results and dispersion relations have obtained through variation approach. Firstly, potential flow theory and perturbation method for linear and weakly nonlinear analysis have been summarized in Chapter 2, and exact results for initial problems of linear RT and KH interface unstable evolution are given, then an improved solution for mass ablation is also concluded.Secondly, it is found in this work for short wavelength perturbations, growth rate for KHI can be enhanced by density gradient, which is a well known stabilizing effect for RTI. A growth rate graph is shown for different density profiles between two stratified fluids with finite-element approach, growth rate formula for KHI with density gradient has been compared with simulation results. Central finite difference methods have been applied to solve the general eigenvalue problems of continual density and velocity state, numerical results also have compared with the approximate formulas.Thirdly, it is also found a density gradient effect has been included in previous models for compressibility discussions; a new model has been set to clarify the effect of compressibility factors from other incompressible factors. It is shown that from approximate dispersion relations, both the specific heat ratio and the interface pressure can enhance the growth rate for fluids under fixed density profile.