On an Equation Related to Nonlinear Saturation of Convection Phenomena.
MARYLAND UNIV COLLEGE PARK INST FOR FLUID DYNAMICS AND APPLIED MATHEMATICS
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A number of problems involving convection-like phenomena give rise to an equation of the form y double prime alphay - 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 alphay - ay y cubed 0 which provides saturation of the dependent variable when y the square root of ab. 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
- Numerical Mathematics
- Fluid Mechanics