Resumen de Rayleigh taylor instability in accelerated high energy density matter
The Rayleigh-Taylor instability has been studied at an interface between an elastic-plastic solid and a Newtonian liquid and the stability region, given by the initial perturbation amplitude ξ0 and wavelength λ, has been determined. The stability region is found to be enhanced by the effect of the liquid viscosity, but it reaches an asymptote for a sufficiently high viscosity. In addition, it is also found that the boundary for the transition from the elastic to the plastic regime get closer to the stability boundary up to both boundaries coincide for a high enough liquid viscosity, thus making the onset of plastic flow a sufficient condition for instability.
The time evolution of the perturbations has also been calculated in terms of the mechanical properties of the solid and the liquid. Four kinds of possible evolutions are found: two stable and two unstable, depending on their positions in the space of parameters (ξ0,λ). All of them present some features that are independent of the solid properties and that are determined only by the liquid viscosity.
The magneto-Rayleigh-Taylor instability at the interface between a Newtonian fluid and an elastic-plastic solid is also performed by considering a uniform magnetic B, parallel to the interface, which has diffused into the fluid but not into the solid. It is found that the magnetic field attributes elastic properties to the viscous fluid which enhance the stability region by stabilizing all the perturbation wavelengths shorter than λ 0 ~ B2 for any initial perturbation amplitude. Longer wavelengths are stabilized by the mechanical properties of the solid provided that the initial perturbation wavelength is smaller than a threshold value determined by the yield strength and the shear modulus of the solid. Beyond this threshold, the amplitude grows initially with a growth rate reduced by the solid strength properties. However, such properties do not affect the asymptotic growth rate which is only determined by the magnetic field and the fluid viscosity. The described physical situation intends to resemble some of the features present in recent experiments involving the magnetic shockless acceleration of flyers plates.
In addition, a model has been developed for the linear Rayleigh-Taylor instability that takes place during the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.
In order to know to know the evolution of the acceleration material behind the shock, a model for the hydrodynamic attenuation (growth and decay) of planar shocks was also developed. The model is based on the approximate integration of the fluid conservation equations, and it does not require the heuristic assumptions used in some previous works. A key issue of the model is that the boundary condition on the piston surface is given by the retarded pressure, which takes into account the transit time of the sound waves between the piston and any position at the bulk of the shocked fluid. The model yields the shock pressure evolution for any given pressure pulse on the piston, as well as the evolution of the trajectories, velocities, and accelerations on the shock and piston surfaces. An asymptotic analytical solution is also found for the decay of the shock wave.
