LINEAR-STABILITY OF THE 3-DIMENSIONAL SEMIGEOSTROPHIC MODEL IN GEOMETRIC COORDINATES

Motivated by the recent work on the stability properties of balanced d ynamics, the author investigates in this paper the stability of parall el, basic how in the baroclinic semigeostrophic (SG) model in geometri c coordinates. The Linearized baroclinic SG equation with a nonconstan t Coriolis parameter is presented. Conservation equations for two wave -activity invariants, analogous to the pseudomomentum and pseudoenergy in baroclinic quasigeostrophic dynamics but with the contributions fr om lateral boundaries, are derived and then used to examine the stabil ity properties of the SG model. It is found that the lateral boundary contributions to the invariants, which were often ignored, are importa nt to the stability mechanism of the SG model. The general properties of normal mode disturbances in the SG model are investigated. Results obtained in this work include an orthogonality relation, the semicircl e theorem to hound the phase speed of normal mode disturbances, and an estimate of upper bound on unstable growth rate.