ON THE LINEARIZATION OF THE EQUATIONS OF HYDRODYNAMICS,
Abstract
The basic problem in hydrodynamic stability is to determine the critical values of the Reynolds number at which the flow becomes unstable. As the equations are nonlinear, it is hard to get any meaningful quantitative information (i.e. numbers) from a direct analysis of them. Accordingly much of the literature in hydrodynamic stability is devoted to an analysis of linearized equations. It is argued that if the perturbations are small then the nonlinear term is of second order magnitude and can be neglected. Of course, this argument is open to question, especially as the nonlinear term involves derivatives of the flow, which may not be small. Nevertheless, a considerable body of experimental evidence tends to support this 'linearization hypothesis,' and the point of this paper is to give a rigorous, general mathematical proof of its validity in the case of a bounded domain. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1965
- Accession Number
- AD0682225
Entities
People
- D. H. Sattinger
Organizations
- University of California, Los Angeles