On an Equation Related to Nonlinear Saturation of Convection Phenomena.
Abstract
A number of problems involving convection-like phenomena give rise to an equation of the form y double prime + (alpha)y' - ay = 0 when the problem is treated in the linear approximation. It is proposed that the description of nonlinear saturation of the convection process requires the introduction of a phenomenological cubic term with a positive coefficient to yield an equation of the form y double prime + (alpha)y' - ay + (y cubed) = 0 which provides saturation of the dependent variable when y = the square root of (a/b). The significance of this term in various physical problems is discussed. In the mathematical analysis of the equation the parameter ranges for oscillatory and non-oscillatory solutions are discussed and related to the pertinent physical problems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1972
- Accession Number
- AD0754228
Entities
People
- Ferdinand Cap
- Herbert Lashinsky
Organizations
- University of Maryland