Long baroclinic planetary waves in a nonzonal vertically sheared mean flow

We consider long planetary waves of annual period linearized about a steady, wind-driven subtropical (ST) gyre circulation. The circulation divides the gyre into an eastern zone (EZ) where only the surface layer is in steady motion and a western zone (WZ) where both the surface and the middle layer are in steady motion because the potential vorticity of the middle layer is assumed to be homogenized. In both zones the upper two layers participate in the wave motion while the deepest third layer is supposed infinitely deep and therefore quiescent.; In the EZ the solution consists of two sets of baroclinic waves, each a combination of the classical first and the second baroclinic Rossby wave coupled by the background flow. In the WZ the propagation of information from the western boundary of the ocean is neglected; therefore the WZ solution consists of only the long set of baroclinic waves.; For sufficiently strong background flow the annual period perturbation solution in the southwestern part of the ST gyre is baroclinically unstable and grows westward. The instability may be generated by local wind forcing or energy incident from the east.; We study the first possibility by analysing perturbations that are generated by a specified initial perturbation or by annual period forcing started at some initial time. Even very gentle nonzonal background flow dramatically changes the waves away from the simple β solutions. In the first case a Gaussian shaped initial disturbance evolves in a highly anisotropic manner. Growth of the amplitude of the transient solution depends strongly on the central wavenumber and spectral width of the initial disturbance. In the latter case the solution consists of a forced part varying at the annual period plus a transient part.