2009 Fiscal Year Final Research Report

Applications of Coulomb wave functions to fluid mechanics.

Research Project

Project/Area Number	19540133
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	Yamaguchi University
Principal Investigator	NISHIYAMA Takahiro Yamaguchi University, 大学院・理工学研究科, 准教授 (60333241)
Project Period (FY)	2007 – 2009
Keywords	クーロン波動関数 / 合流型超幾何関数 / オイラー方程式 / 円管ポアズイユ流
Research Abstract	Coulomb wave functions belong to a family of confluent hypergeometric functions and are mainly used in scattering theories in quantum physics. The aim of the research is to apply them to fluid mechanics. First, the convergence of an orthogonal series whose bases are Stokes stream functions of axisymmetric stationary Euler flows and represented with a Coulomb wave function is studied. As a result, a convergence theorem analogous to that of the Fourier or the Fourier-Bessel series is proved. Next, the distribution of complex phase velocities for small disturbances to pipe Poiseuille flow is analytically explained by using asymptotic forms of a Coulomb wave function with a complex variable and a complex parameter.

(2 results)