Numerical Computation of Helical Waves in a Finite Circular Cylinder Using Chebyshev Spectral Method (Advances in Applied Mathematics and Mechanics, 2024)
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 thedifficulty in analytical formulation, the more feasible strategy to obtain helical wavesis numerical computation. For circular cylinders of finite length, a semi-analyticalmethod 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 transcendequations. In this paper, the numerical computation for helical wave in a finite circularcylinder 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 issignificantly reduced with a new criterion suggested.