Effect Of Initial Amplitude Research Articles

The effect of initial amplitude and convergence ratio on instability development and deposited fluctuating kinetic energy in the single-mode Richtmyer–Meshkov instability in spherical implosions

This paper investigates the growth of perturbations on the inner surface of a dense imploding spherical shell due to hydrodynamic instabilities. The perturbations change in amplitude due to Richtmyer–Meshkov instability and Rayleigh-Taylor instability, geometric convergence, and compressibility. Two mode numbers (ℓ=5,50) and three different perturbation amplitudes (a0=0.1λ,0.01λ,0.001λ) are applied to the surface of the dense inner shell. Two independent codes were used to perform simulations with these six perturbation profiles at four convergence ratios, ranging from 3.6 to 7.3, for a total of 48 cases. The mixing layer amplitudes show good agreement between the two simulation codes across the range of convergence ratios, mode numbers, and initial amplitudes. The growth of the mixing layer is employed to validate an extension of a recently proposed Bell-Plesset model, showing good agreement across the range of convergence ratios. Persistent and substantial shock-deposited fluctuating kinetic energy is observed within the light core, away from the perturbed interface. Temporal evolution of fluctuating kinetic energy indicates a time delay between the peak radial and theta directions, consistent with a build-up of vortical motion. A “jet” like phenomena is observed at the peaks and troughs of the initial perturbations in both simulation codes across a variety of cases. It is postulated that these occur due to the shape singularity shown to develop in spatially periodic perturbed planar shock waves in ideal gas dynamics. Significant anisotropy of kinetic energy components is present at all times.

Dynamic Properties of a Moving Thread Line

A mathematical model representing the transverse vibration of axially moving elastic strings is presented considering tension and mass variation. A suggested numerical scheme was successfully used to solve the nonlinear partial differential equations of motion. For axially nonmoving strings, the effect of initial amplitudes, and consequently the tension variation on the fundamental frequency is obtained. Also, the effect of the initial tension and the mass of the string per unit length on the fundamental frequency and their corresponding mathematical relations are presented. For axially moving strings, the effect of the axial velocity on the fundamental frequency as well as the tension distribution along the thread is given. Also the behavior of the string at velocities equal and greater than the wave speed is shown.