Energy Partition of Equatorial Waves Excited by Various Initial Imbalances in the Linearized Shallow-Water Equation System on the Equatorial Beta Plane

Abstract

   It is important to understand the energy partition between quasi-geostrophic (QG) and non-geostrophic (NG) components for various initial imbalances in large-scale atmosphere-ocean dynamics (geostrophic adjustment). This has been well studied on the midlatitude f plane but is not understood in the equatorial regions, where several equatorial waves are excited simultaneously.
   By utilizing a linearized shallow-water equation system on the equatorial beta plane (β system), we estimated the energy of equatorial waves for initial imbalances and studied the geostrophic adjustment over the equator. Five types of initial imbalances (pressure, eastward velocity u, northward velocity v, divergence, and vorticity), whose horizontal forms are composed of exp (-x²/λ²) D_n(y) (n=1, 2), are adopted. Here, x(y) denotes an eastward (northward) coordinate, λ a representative scale of the initial imbalance in the x direction, and D_n(y) a parabolic cylinder function of an order n. Equatorial waves are classified into two groups: QG waves, which have many geostrophic properties (a Rossby wave, a large-scale Kelvin wave, and a mixed Rossby-gravity wave close to the Rossby wave) and NG waves, which have many NG properties (an inertial gravity wave, a small-scale Kelvin wave, and a mixed Rossby-gravity wave close to the inertial gravity wave).
   Our study shows that the QG equatorial waves are preferentially excited when λ is large for the pressure and u imbalance cases, and small for the v and vorticity imbalance cases. For the divergence imbalance case, most waves are NG. The characteristic features of the geostrophic adjustment in the β system are similar to those on the midlatitude f plane, confirming that the energy partition rule between QG and NG components is common all over the globe.