Nonlinear interactions between semigeostrophic waves of the Eady type

Abstract

Abstract Baroclinically unstable Eady waves representing solutions of a two-dimensional, uniform potential vorticity, semigeostrophic model are considered. These semigeostrophic waves are expressed as linear solutions in geostrophic coordinate space (X,Z,T), but they satisfy a nonlinear advection equation in physical space (x,z,t). The transformation of the velocity v(X,Z,T) into a physical space solution v(x,z,t) is accomplished by an approximate technique that represents a truncation at second-order in the Rossby number. Two nonlinear processes are delineated: there is nonlinearity inherent in the transformation (X,Z,T)→(x,z,t), and there are nonlinear interactions between the waves. Solutions, representing the interaction of two semigeostrophic waves, are determined for initial conditions that span a range of wave-numbers. Under these conditions both single and double frontal structures (one or two concentrated cyclonic shear zones) can develop. The most significant nonlinear interactions between the u...