Hydrodynamics and Nonlinear Instabilities

  title={Hydrodynamics and Nonlinear Instabilities},
  author={Claude Godr{\`e}che and Paul Manneville},
Preface Overview 1. An introduction to hydrodynamics Bernard Castaing 2. Hydrodynamical instabilities in open flows P. Huerre and M. Rossi 3. Asymptotic techniques in nonlinear problems: some illustrative examples Vincent Halim 4. Pattern forming instabilities Stephan Fauve 5. An introduction to the instability of flames, shocks and detonations G. Joulin and P. Vidal. 
Convective instability on a crystal surface
The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this
Combustion Waves and Fronts in Flows: Flames, Shocks, Detonations, Ablation Fronts and Explosion of Stars
Description: Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of
Convective and absolute instabilities in counter-rotating spiral Poiseuille flow
We present results of an experimental study on the stability of Taylor–Couette flow in case of counter-rotating cylinders and an imposed axial through flow. We are able to confirm results form recent
Theory of the corrugation instability of a piston-driven shock wave.
  • J. Bates
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2015
The two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state is analyzed and small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time.
Instability of isolated planar shock waves
Previously, expressions governing the temporal evolution of linear perturbations to an isolated, planar, two-dimensional shock front in an inviscid fluid medium with an arbitrary equation of state
Viscous Flow Instability of Inflectional Velocity Profile
Rayleigh showed that inviscid flow is unstable if the velocity profile has an inflection point in parallel flows. However, whether viscous flows is unstable or not is still not proved so far when
Instabilities of Wavy Patterns Governed by Coupled Burgers Equations
It is shown that the system of coupled Burgers equations reveals several new types of instabilities, which are studied both analytically and numerically.