Equatorially Bounded Zonally Propagating Linear Waves on a Generalized β Plane

Abstract

Meridionally confined zonally propagating wave solutions to the linear hydrostatic Boussinesq equations on a generalized equatorial ? plane that includes the ?nontraditional? Coriolis force terms associated with the poleward component of planetary rotation are calculated. Kelvin, Rossby, inertia?gravity, and mixed Rossby?gravity modes generalize from the traditional model with the dispersion relation unchanged. The effects of the nontraditional terms on all waves are the curving upward with latitude of the surfaces of constant phase and the equatorial trapping width of the solutions (the equatorial radius of deformation) increasing by order (Ω/N)2 compared to the traditional case, where Ω is the planetary rotation rate and N the buoyancy frequency. In addition, for the Rossby, inertia?gravity, and mixed Rossby?gravity modes, there is a phase shift of O(Ω/N) in the zonal and vertical velocity components relative to the meridional component, and their spatial structures are further modified by differences of O(Ω/N)2. For the Rossby and inertia?gravity waves, the modifications depend also on the phase speed of the wave. In the limit N ? Ω, the traditional approximation is justified and lines of constant phase in the y?z plane become horizontal, whereas for N ? Ω phase lines become everywhere almost parallel to the planetary rotation vector. In both limits, the phase lines are perpendicular to the dominant restoring force?respectively, gravity and the centrifugal force associated with the solid-body rotation of the atmosphere at rest in the rotating frame.