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Abstract. Barotropic slope currents following isobaths are common features of shelf seas in nonequatorial regions. They are usually remotely forced and stabilized locally by the bottom slope. The stability of these barotropic currents is investigated to determine how well they can be modeled numerically as stationary flows. Both prograde jets, with their cyclonic flank in the deeper water, and retrograde jets, with their cyclonic flank in shallower water, are considered. A necessary condition for instability is at least one extremum in the distribution of the potential vorticity across the jet, which is equivalent to the planetary beta stability problem, and corresponds to the well-known Rayleigh inflection-point theorem for the stability problem of a nongeophysical flow. A criterion for instability that involves the bottom slope parameter as a stabilizing factor and the velocity shear as a destabilizing factor has been derived. This criterion suggests that even mild slopes are capable of stabilizing both prograde and retrograde jets. For the case of a cosine jet along an exponential topography, neutral solutions are found to be governed by the Mathieu equation. Because of our use of exponential topography our equation contains more terms than the instability problem for planetary beta on a flat bottom, but the difference tends to vanish when the Rossby number is small. Our results also imply that a given bottom slope stabilizes more wave modes for a retrograde jet, which flows in a direction opposite to topographic Rossby waves. It is evident that these topographically steered currents are predominantly barotropic, so diagnostic constraints in numerical models must include the imposed surface slope, which is an unknown in most cases. All the models mentioned were run to steady state, which rules out the possibility of flow instabilities and/or time-dependent meandering.It is the purpose here to present a theoretical analysis of the stability of both prograde and retrograde forced barotropic slope currents to determine how realistic stationary solutions are, both for flow along the Svalbard Bank and other similar (nonequatorial) seas around the world. An analysis of the equation of motion shows that both the nonlinear and the friction terms are much less than the Coriolis term for the flow along the Svalbard Bank [Li, 1995]. The present work applies therefore to the limit of vanishingly small viscosity. Effects of both bottom friction and wind forcing were considered by Li and McClimans [1998].Most of the recent work on stability in geophysical applications has been numerical because the general problem is hardly tractable analytically. Of relevance to the present study, Send [1989] applied a piecewise uniform potential vorticity to study the stability of barotropic slope currents off California. This approximation was used earlier by Collings and Grimshaw [1984]. Ohshima [1987] criticized this approach on the grounds that the instability is quite sensitive to the jumps between the uniform patches and formulate...

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