• Corpus ID: 119200247

Variational Approach to Necessary and Sufficient Stability Conditions for Inviscid Shear Flow

  title={Variational Approach to Necessary and Sufficient Stability Conditions for Inviscid Shear Flow},
  author={Makoto Hirota and Philip J. Morrison and Yuji Hattori},
  journal={arXiv: Fluid Dynamics},
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh equation are shown to be associated with positive eigenvalues of a certain selfadjoint operator. The stability is therefore simply determined by maximizing a quadratic form, which is theoretically and numerically more tractable than directly solving the… 
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Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations

The aim of this book is to provide a Discussion of the Foundations of Hamiltonian Hopf Bifurcation and its Applications in Fluid Fluid-Elastic Instabilities, as well as some suggestions on how to improve the quality of the analysis.



Mathematical Methods of Classical Mechanics

Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid

Hamiltonian description of shear flow


  • Publ. 17
  • 1950


  • Wiss Fachgruppe, Gottingen, Math. Phys., 1
  • 1935