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Revisiting the Charney Baroclinic Instability Problem and Point-jet Barotropic Instability Problem, Part II: Matched Asymptotic Expansions & Overreflection Without Delta-Functions by John P. Boyd is a scholarly article available to read on EtoBox.

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Baroclinic instability generates the cyclones and anticyclones of midlatitude weather. Charney developed the rst e ective theory for the infancy of this cyclogenesis in 1947. His linear eigenproblem is analytically solvable by con uent hypergeometric functions. It is also, with extension of the domain of the coordinate from [ , ∞] to [-∞, ∞] by re ection about the origin, the point-jet model of barotropic instability, important for tropical cyclogenesis. (Note that the coordinate is height z in the Charney model, but latitude y for the point-jet bartropic instability. It is a great simpli cation that the Charney and point-jet instability problems are mathematically identical, but it also is confusing that the mathematical analysis in y also applies to the Charney problem with the substitution of z for y.) Unfortunately, the theory is full of distributions like the Dirac delta-function and the re ected Charney eigenfunction has a discontinuous rst derivative at y = . Here we regularize the Charney problem by replacing a linear mean current, U = |y|, by either U = ε log(cosh(y/ε)) or U = ε y erf(y/ε), followed by matched asymptotic perturbation expansions in powers of the small regul

Author

John P. Boyd

Publisher

Portico

Published

2018

Language

EN