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Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity…
There is renewed interest in direct-drive inertial confinement fusion, following the milestone December 2022 3.15 MJ ignition result on the National Ignition Facility. A key obstacle is the control of the two plasmon decay instability.…
The influence of the small scale ``cellular'' structure of premixed flames on their evolution at larger scales is investigated. A procedure of the space-time averaging of the flow variables over flame cells is introduced. It is proved that…
The linear stability analysis of an optically thin plasma where a general reaction proceeds, including chemical relaxation time effects, is carried out . A fifth order dispersion equation (instead of the fourth order one resulting when such…
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
This article presents a numerical analysis of the instability developing in horizontally sheared Poiseuille flow, when stratification extends along the vertical direction. Our study builds up on the previous work that originally detected…
This work is devoted to the study of the influence of temperature anisotropy and parallel heat flux on the stability of supersonic shear flow in collisionless plasmas. Within a fluid-based framework, we employ the 16-moment transport…
We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…
Thermodiffusive instabilities can have a leading order effect on flame propagation for lean premixed hydrogen flames. Many simulation studies have been performed to study this effect, but almost exclusively in two-dimensional (2D) or domain…
Shear flows have an important impact on the dynamics in an assortment of different astrophysical objects including accreditation discs and stellar interiors. Investigating shear flow instabilities in a polytropic atmosphere provides a…
In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…
Aims. We aim to determine how ion neutral coupling and ambipolar diffusion affect the linear and the nonlinear growth of the RTinstability under astrophysically relevant conditions, and to identify the coupling regimes in which departures…
The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…
We investigate the nature of dissipative instability appearing in a prominence planar thread filled with partially ionised plasma in the incompressible limit. The importance of partial ionisation is investigated in terms of the ionisation…
The competition between the drive and stabilization of plasma microinstabilities by sheared flow is investigated, focusing on the ion temperature gradient mode. Using a twisting mode representation in sheared slab geometry, the…
We present a generalized hydrodynamic stability theory for interacting particles in polydisperse particle-laden flows. The addition of dispersed particulate matter to a clean flow can either stabilize or destabilize the flow, depending on…
The phenomenon of Taylor or shear-induced dispersion of a non-passive scalar field in a pulsatile pipe flow is investigated, accounting for the scalar field's influence on fluid density and transport coefficients. By employing multiple…
Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of classes of equations. However, these are typically specialized to…
The main characteristics of the linear Darrieus-Landau instability in the laser ablation flow are investigated. The dispersion relation of the instability is found numerically as a solution to an eigenvalue stability problem, taking into…
Turbulent mixing is a physical process of fundamental importance in high-speed premixed flames. This mixing results in enhanced transport of temperature and chemical scalars, leading to potentially large changes in flame structure and…