Related papers: Dissipative instability of shock waves
Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the…
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…
Density-wave fronts in a vibrofluidized wet granular layer undergoing a gas-liquid-like transition are investigated experimentally. The threshold of the instability is governed by the amplitude of the vertical vibrations. Fronts, which are…
This paper concerns the stabilizing effect of viscosity on the vortex sheets. It is found that although a vortex sheet is not a time-asymptotic attractor for the compressible Navier-Stokes equations, a viscous wave that approximates the…
The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is…
We study analytically and numerically the stability of the standing waves for a nonlinear Schr\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the…
The transition from laminar to turbulent flow has been a notorious riddle in fluid dynamics since the nineteenth century. Hydrodynamic instabilities were regarded as a cause for the onset of turbulence, but their theoretical investigation…
A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic stability of the viscous shock wave is established under some smallness conditions. The proof is given by an elementary…
In dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom…
The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas…
In this paper we investigate gravitational instability of shocked gas layers using linear analysis. An unperturbed state is a self-gravitating isothermal layer which grows with time by the accretion of gas through shock fronts due to a…
In several space dimensions, scalar shock waves between two constant states u $\pm$ are not necessarily planar. We describe them in detail. Then we prove their asymptotic stability, assuming that they are uniformly non-characteristic. Our…
In a computational study we reveal a novel dynamical instability of excitation waves in the heartmuscle. The instability manifests itself as gradual local increase in the duration of the actionpotential which causes formation and…
In this paper we study the lateral instability of streamer discharges using a continuum discharge model. We observe similarities to Kelvin-Helmholz instability in fluids. In strong electric fields, lateral long wave length perturbations can…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
The growth rate of long wavelength kinetic instabilities arising due to the interaction of a collimated beam of relativistic particles and a cold unmagnetized plasma are calculated in the ultra relativistic limit. For sufficiently…
Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport…