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The convective instability in a plane liquid layer with time-dependent temperature profile is investigated by means of a general method suitable for linear stability analysis of an unsteady basic flow. The method is based on a non-normal…
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here we show that finite inertia of individual…
We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a…
We investigate the asymptotic stability of standing waves for a model of Schr\"odinger equation with spatially concentrated nonlinearity in space dimension three. The nonlinearity studied is a power nonlinearity concentrated at the point…
The Rayleigh-Taylor instability plays an important role in the dynamics of several astronomical objects, in particular, in supernovae (SN) evolution. In this paper we develop an analytical approach to study the stability analysis of…
This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal…
Several simulations of turbulence in the Large Plasma Device (LAPD) [W. Gekelman et al., Rev. Sci. Inst. 62, 2875 (1991)] are energetically analyzed and compared with each other and with the experiment. The simulations use the same model,…
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemann's invariant that is related to the wave…
We study the modes and stability of non - isothermal coronal loop models with different intensity values of the equilibrium magnetic field. We use an energy principle obtained via non - equilibrium thermodynamic arguments. The principle is…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results…
Thermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast…
During stellar core collapse, which eventually leads to a supernovae explosion, the stalled shock is unstable due to the standing accretion shock instability (SASI). This instability induces large-scale non spherical oscillations of the…
Magnetoacoustic oscillations are nowadays routinely observed in various regions of the solar corona. This allows them to be used as means of diagnosing plasma parameters and processes occurring in it. Plasma diagnostics, in turn, requires a…
The linear stability of isothermal Bondi accretion with a shock is studied analytically in the asymptotic limit of high incident Mach number M_1. The flow is unstable with respect to radial perturbations as expected by Nakayama (1993), due…
We consider the problem of dynamical stability for the $n$-vortex of the Ginzburg-Landau model. Vortices are one of the main examples of topological solitons, and their dynamic stability is the basic assumption of the asymptotic ``particle…
Global linear stability analysis of a self-similar solution describing the interaction of a relativistic shell with an ambient medium is performed. The solution is shown to be unstable to convective Rayleigh-Taylor modes having angular…
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture,…
A Langmuir wave (LW) model is constructed whose equilibria are consistent with stimulated Raman scatter optimization, with Hamiltonian dynamics and with rotational invariance. Linear instability analysis includes terms to all orders in wave…
We investigate the perturbation dynamics in a supersonic shear layer using a combination of large-eddy simulations (LES) and linear-operator-based input-output analysis. The flow consists of two streams-a main stream (Mach 1.23) and a…