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Boyd, J. P.

Publications and source records attributed to Boyd, J. P..

8 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

The influence of meridional shear on planetary waves. I - Nonsingular wind profiles. II - Critical latitudes

An attempt to define a relationship between the strength and curvature of the latitudinal wind shear and the planetary waves is presented. Previous work based on the WKB method is reviewed and compared with Galerkin's method, which is found to be effective when considering low-order modes. The WKB method, however, increases in accuracy with the mode number. Both methods are applied to a linear wind shear profile and the Galerkin method is determined to be significantly superior in predicting the lowest order, and is therefore suitable for formulating the latitudinal structure of quasi-stationary Rossby waves in the middle atmosphere. In a second paper the mean zonal wind is assumed to depend on latitude only, and the effects of critical latitudes, where the Doppler shifter frequency is zero, on planetary waves are shown to include shear-induced instability in Kelvin waves. Further research to assay the extent that baroclinity alters stable winds is indicated.

Boyd, J. P.↗
NASA NTRS1982

The optimization of convergence for Chebyshev polynomial methods in an unbounded domain

Grosch and Orszag (1977) have performed a numerical analysis of the problem of solving differential equations in a semiinfinite or infinite domain using Chebyshev polynomials. The principal limitation of the conducted study was that it was entirely empirical. Various differential equations were solved in different ways and the numbers were compared. The present investigation has the objective to extend the studies conducted by Grosch and Orszag by deriving asymptotic approximations to the Chebyshev coefficients of simple model functions. This approach makes it possible to conduct more systematic comparisons of different methods, extend the range of comparisons, and, perhaps most important, give simple analytic formulas for choosing the optimum domain size or mapping parameter L for various situations.

Boyd, J. P.↗
NASA NTRS1981

Sturm-Liouville eigenproblems with an interior pole

The eigenvalues and eigenfunctions of self-adjoint Sturm-Liouville problems with a simple pole on the interior of an interval are investigated. Three general theorems are proved, and it is shown that as n approaches infinity, the eigenfunctions more and more closely resemble those of an ordinary Sturm-Liouville problem. The low-order modes differ significantly from those of a nonsingular eigenproblem in that both eigenvalues and eigenfunctions are complex, and the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. In addition, the WKB is shown to be accurate for all n, and all eigenvalues of a normal one-dimensional Sturm-Liouville equation with nonperiodic boundary conditions are well separated.

Boyd, J. P.↗
NASA NTRS1981

Analytic approximations to the modon dispersion relation

Three explicit analytic approximations are given to the modon dispersion relation developed by Flierl et al. (1980) to describe Gulf Stream rings and related phenomena in the oceans and atmosphere. The solutions are in the form of k(q), and are developed in the form of a power series in q for small q, an inverse power series in 1/q for large q, and a two-point Pade approximant. The low order Pade approximant is shown to yield a solution for the dispersion relation with a maximum relative error for the lowest branch of the function equal to one in 700 in the q interval zero to infinity.

Boyd, J. P.↗
NASA NTRS1980

The nonlinear equatorial Kelvin wave

Using the method of strained coordinates, a uniformly valid approximation to the nonlinear equatorial Kelvin wave is derived. It is shown that nonlinear effects are negligible for the Kelvin waves associated with the Gulf of Guinea upwelling. The Kelvin waves involved in El Nino, however, are significantly distorted both in shape and speed. The leading edge is smoothed and expanded rather than steepened, but the trailing edge will form sharp fronts and eventually break.

Boyd, J. P.↗