Parametric Expansions with Hermite and Laguerre Polynomials and Their Application to Unstable and Turbulent Flows.
Scientific rept. no. 2,
BOSTON UNIV MA CENTER FOR SPACE PHYSICS
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We consider an approximation method parametric expansion, based on the classical Hermite and Laguerre polynomials. Our method modifies the classical basis functions with adjustable-width exponential factors. The width is a free parameter that is used to optimize convergence. We apply the expansion to the fluid equations for models of free sheared atmospheres. We find that the new expansion does not reveal unstable modes. In Appendix 1, the advantages of parametric expansions are illustrated by the deblurring of images corrupted by turbulence. In Appendix 2, the structure of turbulent shear flows is analyzed by applying our expansion to the appropriate two-point correlation function. Parametric expansion, Free sheared atmosphere, Turbulent shear flow.
- Fluid Mechanics
- Numerical Mathematics