Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 8 1/2 2001 10.5194/npg-8-21-2001 http://www.nonlin-processes-geophys.net/8/21/2001/ http://www.nonlin-processes-geophys.net/8/21/2001/npg-8-21-2001.html http://www.nonlin-processes-geophys.net/8/21/2001/npg-8-21-2001.pdf 21 36 0000-00-00 Bifurcations and instabilities in rotating two-layer fluids: I.f-plane A. F. Lovegrove I. M. Moroz P. L. Read Atmospheric, Oceanic & Planetary Physics, University of Oxford, United Kingdom Mathematical Institute, University of Oxford, United Kingdom Present address: Smiths System Engineering, Guildford, UK In this paper, we show that the behaviour of weakly nonlinear waves in a 2-layer model of baroclinic instability on an f-plane with varying viscosity is determined by a single, degenerate codimension three bifurcation. In the process, we show how previous studies, using the method of multiple scales to derive evolution equations for the slowly varying amplitude of the growing wave, arise as special limits of the general evolution description. A companion study will extend the results to a <i>&#946;</i>-plane.