Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method

Helical waves are eigenfunctions of the curl operator and can be used to decompose an arbitrary three-dimensional vector field orthogonally. In turbulence study, high accuracy for helical waves especially of high wavenumber is required. Due to the difficulty in analytical formulation, the more feasible strategy to obtain helical waves is numerical computation. For circular cylinders of finite length, a semi-analytical method via infinite series to formulate the helical wave is known [E. C. Morse, J. Math. Phys., 46 (2005), 113511], where the eigenvalues are evaluated by iterating transcend equations. In this paper, the numerical computation for helical wave in a finite circular cylinder is implemented using a Chebyshev spectral method. The solving is transformed into a standard matrix eigenvalue problem. The large eigenvalues are computed with high precision, and the calculation cost to rule out spurious eigenvalues is significantly reduced with a new criterion suggested.