A case study of methods of series summation: KelvinHelmholtz instability of finite amplitude
We compute the singularities of the solution of the BirkhoffRott equation that governs the evolution of a planar periodic vortex sheet. Our approach uses the Taylor series obtained by Meiron et al. [J. Fluid Mech. 114 (1982) 283] for a flat sheet subject initially to a sinusoidal disturbance of amplitude a. The series is then summed by using various generalisations of the Pad method. We find approximate values for the location and type of the principal singularity as a ranges from zero to infinity. Finally, the results are used as a basis to guide the choice of methods of summing series arising from problems in fluid mechanics.
series summation kelvinhelmholtz instability birkhoffrott equation hermitepad approximation