Stability Analysis for an Interface with a Continuous Internal Structure

Mikhail Modestov

doi:10.3390/fluids6010018

Abstract

A general method for solving a linear stability problem of an interface with a continuous internal structure is described. Such interfaces or fronts are commonly found in various branches of physics, such as combustion and plasma physics. It extends simplified analysis of an infinitely thin discontinuous front by means of numerical integration along the steady-state solution. Two examples are presented to demonstrate the application of the method for 1D pulsating instability in magnetic deflagration and 2D Darrieus–Landau instability in a laser ablation wave.

Highlights

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This paper is devoted to a method of solving the stability problem at the interface with a realistic continuous internal structure
The above modes and eigenvectors constitute the boundary conditions for the numerical integration of the system (2) along the steady-state profile

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The RT instability in inertial confinement fusion distorts the pellet symmetry, decreasing the fuel compression and limiting the net gain of nuclear reaction [3] This was confirmed experimentally, but the instability evolves at a much slower pace than that estimated with the discontinuity approach. A typical example is to assume an exponential density profile in studies of various instabilities in plasma physics [2,5] Very often, such a consideration requires an additional matching condition at the front. This paper is devoted to a method of solving the stability problem at the interface with a realistic continuous internal structure It eliminates the problem of the extra matching condition by integrating the perturbed equations along the continuous profile of the steadystate solution.

General Algorithm

One-Dimensional Pulsating Instability in Molecular Magnets

Two-Dimensional Darrieus–Landau Instability in Laser Ablation

Discussions and Conclusions