On the numerical dispersion relation of equatorial waves

Abstract

Numerical dispersion relations for equatorial wave modes are computed two ways: from equations for the pressure, p, and for the meridional velocity, v. These are compared with both the continuous and the analytic finite difference dispersion relations for the u‐v‐p system of equations on an Arakawa C‐grid derived by D. W. Moore (personal communication, 1990). For a particular meridional wave structure and grid resolution, the dispersion relation is approximated more accurately via the finite‐difference form of the v‐equation than by either the p‐equation or the u‐v‐p system. However, the finite difference v‐equation possesses an undesirable wave solution which has unbounded u and p, and it also lacks the equatorial Kelvin wave. On the other hand, the p‐equation, is found to possess additional numerical solutions due to the conversion of the apparent singularities of the continuous equation at the inertial latitudes (yil = ±σ/β) into regular singularities of the discrete equation due to numerical truncation. These additional solutions are well separated in dispersion space from the equatorial ones except at selected frequencies. The frequencies at which the wavelengths of these additional solutions to the p‐equation approach the continuous dispersion relations are found to be sensitive to the distance from the inertial latitude to the nearest gridpoint.