Singular Eigenfunctions and an Integral Transform for Shear Flow
Euler’s equation linearized about a shear flow equilibrium is solved by means of a novel invertible integral transform that is a generalization of the Hilbert transform. The integral transform provides a means for describing the dynamics of the continuous spectrum that is well-known to occur in this and other systems. The results are interpreted briefly in the context of infinite dimensional Hamiltonian systems theory, which serves as a unifying principle.
KeywordsShear Flow Continuous Spectrum Integral Transform Linear Dynamic Hamiltonian Structure
Unable to display preview. Download preview PDF.
- 3.N.J. Balmforth and P.J. Morrison: ‘Hamiltonian Description of Shear Flow’. In Large-Scale Atmosphere-Ocean Dynamics I +II. ed. by J. Norbury and I. Roulstone (Cambridge, Cambridge 2002) pp. 117–142Google Scholar
- 7.L. Engevik: ‘On the stability problem in hydrodynamics’. Dept. Applied Math. Bergen, Norway, Pub. No. 11 (1966).Google Scholar
- 8.I.M. Gel’fand: Generalized Functions (Academic, New York 1964)Google Scholar