Premium
Spectral approximation in the numerical stability study of nondivergent viscous flows on a sphere
Author(s) -
Skiba Yuri N.
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199803)14:2<143::aid-num1>3.0.co;2-o
Subject(s) - mathematics , mathematical analysis , eigenvalues and eigenvectors , zonal spherical harmonics , fourier series , rate of convergence , spherical harmonics , solid harmonics , flow (mathematics) , spin weighted spherical harmonics , geometry , vector spherical harmonics , harmonics , channel (broadcasting) , physics , quantum mechanics , voltage , electrical engineering , engineering
The accuracy of calculating the normal modes in the numerical linear stability study of two‐dimensional nondivergent viscous flows on a rotating sphere is analyzed. Discrete spectral problems are obtained by truncating Fourier's series of the spherical harmonics for both the basic flow and the disturbances to spherical polynomials of degrees K and N , respectively. The spectral theory for the closed operators [1], and embedding theorems for the Hilbert and Banach spaces of smooth functions on a sphere are used to estimate the rate of convergence of the eigenvalues and eigenvectors. It is shown that the convergence takes place if the basic state is sufficiently smooth, and the truncation numbers K and N of Fourier's series for the basic flow and disturbances tend to infinity keeping the ratio N / K fixed. The convergence rate increases with the smoothness of the basic flow and with the power s of the Laplace operator in the vorticity equation diffusion term. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14:143–157, 1998