ELSEVIER Dynamics of Atmospheres and Oceans 27 (1997) 81-90 and oceans Nonlinear spatial baroclinic instability in slowly varying zonal flow Terrence R. Nathan Atmospheric Science Program, Department of Land, Air and Water Resources, University of California, Davis, CA 95616, USA Received 30 December 1995; revised 11 October 1996; accepted 22 November 1996 Abstract The linear and weakly nonlinear dynamics of long, low frequency, spatially growing baroclinic waves embedded in slowly varying zonal flow on a/3-plane channel are examined in a continuous model of the atmosphere. For a basic state jet flow possessing a locally unstable region, the nonlinear solution yields a maximum amplitude that is located near the region of maximum baroclinicity and substantially upstream of the maximum amplitude obtained from linear theory. The difference between the linear and nonlinear solutions is due to the time-averaged wave fluxes becoming large enough in the nonlinear problem to stabilize the flow prior to reaching the location (jet center) where the basic state baroclinicity and locally computed linear growth rate are maximized. © 1997 Elsevier Science B.V. I. Introduction Spatial instabilities are characterized by growth in space rather than time. Their excitation hinges on the generation of disturbances by a localized wave maker with real frequency. Studies (e.g. Hogg, 1976, Thacker, 1976, Li and Nathan, 1994, 1997) have shown that spatial instabilities likely play an important role in the circulations of both the ocean and atmosphere. In an oceanic context, Hogg (1976) has hypothesized that rough topography in the vicinity of Cape Hatteras can act as a wave maker by producing localized temporal fluctuations in the flow. Using a simple linear baroclinic model with fixed forcing frequency, Hogg demonstrated that spatial instabilities indeed emerge that have charac- teristics similar to the strong small-scale motions observed in the vicinity of the Gulf Stream. In an atmospheric context, Li and Nathan (1994) have shown using a linear, spherical 0377-0265//97//$17.00 © 1997 Elsevier Science B.V. All rights reserved. PH S0377-0265(97)00002-X