Stability of Viscous St. Venant Roll Waves: From Onset to Infinite Froude Number Limit

[1]  S. Benzoni-Gavage,et al.  Co-periodic stability of periodic waves in some Hamiltonian PDEs , 2015, 1505.01382.

[2]  L. Miguel Rodrigues,et al.  Periodic-Coefficient Damping Estimates, and Stability of Large-Amplitude Roll Waves in Inclined Thin Film Flow , 2015, SIAM J. Math. Anal..

[3]  Blake Barker,et al.  STABLAB Documentation for KdV : Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow , 2014, ArXiv.

[4]  L. Miguel Rodrigues,et al.  Slow Modulations of Periodic Waves in Hamiltonian PDEs, with Application to Capillary Fluids , 2013, Journal of Nonlinear Science.

[5]  Mathew A. Johnson,et al.  Modulational Instability in the Whitham Equation for Water Waves , 2013, 1312.1579.

[6]  Todd Kapitula,et al.  Spectral and Dynamical Stability of Nonlinear Waves , 2013 .

[7]  S. Gavrilyuk,et al.  The classical hydraulic jump in a model of shear shallow-water flows , 2013, Journal of Fluid Mechanics.

[8]  Mathew A. Johnson,et al.  Nonlinear modulational stability of periodic traveling-wave solutions of the generalized Kuramoto–Sivashinsky equation , 2012, 1203.3795.

[9]  P. Noble,et al.  Whitham's Modulation Equations and Stability of Periodic Wave Solutions of the Korteweg-de Vries-Kuramoto-Sivashinsky Equation , 2013 .

[10]  Mathew A. Johnson,et al.  Behavior of periodic solutions of viscous conservation laws under localized and nonlocalized perturbations , 2012, 1211.2156.

[11]  S. Gavrilyuk,et al.  A new model of roll waves: comparison with Brock’s experiments , 2012, Journal of Fluid Mechanics.

[12]  Mathew A. Johnson,et al.  Spectral stability of periodic wave trains of the Korteweg-de Vries/Kuramoto-Sivashinsky equation in the Korteweg-de Vries limit , 2012, 1202.6402.

[13]  L. Miguel Rodrigues,et al.  Stability of periodic Kuramoto-Sivashinsky waves , 2010, Appl. Math. Lett..

[14]  Kevin Zumbrun,et al.  Convergence of Hill's Method for Nonselfadjoint Operators , 2010, SIAM J. Numer. Anal..

[15]  Mathew A. Johnson,et al.  Metastability of solitary roll wave solutions of the St. Venant equations with viscosity , 2010, 1007.5262.

[16]  Kevin Zumbrun,et al.  Nonlinear Stability of Viscous Roll Waves , 2010, SIAM J. Math. Anal..

[17]  Kevin Zumbrun,et al.  Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two , 2009, SIAM J. Appl. Dyn. Syst..

[18]  T. Kapitula,et al.  The orbital stability of the cnoidal waves of the Korteweg-de Vries equation , 2010 .

[19]  Mathew A. Johnson,et al.  Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law , 2010, 1008.4729.

[20]  Mathew A. Johnson,et al.  Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case , 2010, 1001.0404.

[21]  Bernard Deconinck,et al.  On the convergence of Hill's method , 2010, Math. Comput..

[22]  Bernard Deconinck,et al.  KdV cnoidal waves are spectrally stable , 2009 .

[23]  K. Zumbrun Numerical error analysis for Evans function computations: a numerical gap lemma, centered-coordinate methods, and the unreasonable effectiveness of continuous orthogonalization , 2009, 0904.0268.

[24]  K. Zumbrun,et al.  Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions , 2008, 0810.4130.

[25]  Todd Kapitula,et al.  On the spectra of periodic waves for infinite-dimensional Hamiltonian systems , 2008 .

[26]  Bernard Deconinck,et al.  SpectrUW: A laboratory for the numerical exploration of spectra of linear operators , 2007, Math. Comput. Simul..

[27]  R. Pego,et al.  Long-time persistence of Korteweg–de Vries solitons as transient dynamics in a model of inclined film flow , 2007, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[28]  Bernard Deconinck,et al.  Computing spectra of linear operators using the Floquet-Fourier-Hill method , 2006, J. Comput. Phys..

[29]  K. Zumbrun,et al.  An efficient shooting algorithm for Evans function calculations in large systems , 2005, math/0508020.

[30]  P. Noble On the spectral stability of Roll-waves , 2006 .

[31]  D. Serre,et al.  Spectral Stability of Periodic Solutions of Viscous Conservation Laws: Large Wavelength Analysis , 2005 .

[32]  V. Liapidevskii,et al.  STABILITY OF REGULAR ROLL WAVES , 2005 .

[33]  Shreyas Mandre,et al.  Dynamics of roll waves , 2004, Journal of Fluid Mechanics.

[34]  Neil B. Morley,et al.  Characterization of the effect of Froude number on surface waves and heat transfer in inclined turbulent open channel water flows , 2003 .

[35]  Jun Yu,et al.  Evolution of Small Periodic Disturbances into Roll Waves in Channel Flow with Internal Dissipation * , 2003 .

[36]  K. Zumbrun,et al.  An Evans function approach to spectral stability of small-amplitude shock profiles , 2002, math/0205180.

[37]  Hsueh-Chia Chang,et al.  Complex Wave Dynamics on Thin Films , 2002 .

[38]  Alexander Mielke,et al.  The Ginzburg-Landau Equation in Its Role as a Modulation Equation , 2002 .

[39]  Björn Sandstede,et al.  On the Stability of Periodic Travelling Waves with Large Spatial Period , 2001 .

[40]  Kevin Zumbrun,et al.  The gap lemma and geometric criteria for instability of viscous shock profiles , 1998 .

[41]  Alexander Mielke,et al.  Instability and Stability of Rolls in the Swift–Hohenberg Equation , 1997 .

[42]  A. Mielke Mathematical analysis of sideband instabilities with application to rayleigh-bénard convection , 1997 .

[43]  R. Gardner,et al.  Spectral analysis of long wavelength periodic waves and applications. , 1997 .

[44]  G. Schneider Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation , 1996 .

[45]  Alexander A. Nepomnyashchy,et al.  Stability of periodic waves governed by the modified Kawahara equation , 1995 .

[46]  D. McLaughlin,et al.  Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis , 1993 .

[47]  Hsueh-Chia Chang,et al.  Laminarizing effects of dispersion in an active-dissipative nonlinear medium , 1993 .

[48]  H. Win Model equation of surface waves of viscous fluid down an inclined plane , 1993 .

[49]  R. Gardner,et al.  ON THE STRUCTURE OF THE SPECTRA OF PERIODIC TRAVELING WAVES , 1993 .

[50]  M. Abd-el-Malek Approximate solution of gravity-affected flow from planar sluice gate at high Froude number , 1991 .

[51]  Pierre Collet,et al.  Instabilities and fronts in extended systems , 1990 .

[52]  G. I. Siv Ashinsky,et al.  Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations , 1988 .

[53]  S. Hwang,et al.  Turbulent and inertial roll waves in inclined film flow , 1987 .

[54]  Uriel Frisch,et al.  Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model , 1986, Journal of Fluid Mechanics.

[55]  E. Kuznetsov,et al.  On the stability of nonlinear waves in integrable models , 1984 .

[56]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[57]  G. Sivashinsky,et al.  Instabilities, Pattern Formation, and Turbulence in Flames , 1983 .

[58]  Yoshiki Kuramoto,et al.  On the Formation of Dissipative Structures in Reaction-Diffusion Systems Reductive Perturbation Approach , 1975 .

[59]  R. R. Brock,et al.  Development of Roll-Wave Trains in Open Channels , 1969 .

[60]  R. Dressler,et al.  Mathematical solution of the problem of roll-waves in inclined opel channels , 1949 .

[61]  Harold Jeffreys M.A. D.Sc. LXXXIV. The flow of water in an inclined channel of rectangular section , 1925 .