A Note on Elliptical Modons

Abstract

   For any stationary solution of the potential vorticity equation, the streamfunction Ψ and the potential vorticity Q are functionally related, i.e., Q=F (Ψ). For analytical modons which are considered as one of the models of atmospheric blocking, the functional form of Q=F (Ψ) is assumed to be linear and therefore the modon boundary is assumed to be circular. Modons with boundaries other than a circle have been numerically investigated by several authors. Boyd and Ma (1990) calculated numerically the functional form of Q=F (Ψ) for elliptical modons elongated in the basic flow direction on an ƒ plane. In this note, the functional form of Q=F (Ψ) is calculated analytically for modons with an elliptical boundary slightly different from a circle. For modons elongated in the basic flow direction, the result agrees qualitatively with the above-mentioned numerical one. On the other hand, for modons elongated in the direction perpendicular to the basic flow, the functional form of Q=F (Ψ) is shown to be qualitatively different from that for modons elongated in the basic flow.