## 1. Introduction

[2] A forced-planetary vorticity balance often invoked in the theories of the large-scale flow in a flat-bottomed ocean is the Sverdrup balance, i.e., a balance between the vortex tube squashing by the surface Ekman pumping and the advection of planetary vorticity by the geostrophic transport [e.g., *Pedlosky*, 1996]. On the other hand, a geostrophic flow over a sloping bottom in an area with a small variation of the Coriolis parameter is likely to be in a vorticity balance between the bottom Ekman pumping and the vortex tube stretching by the cross-isobath bottom geostrophic flow. The motion associated with such a frictional-topographic vorticity balance is often referred to as the arrested topographic wave (ATW). The original ATW model was constructed by *Csanady* [1978] from steady equations for a net (depth-averaged), wind-driven flow in a coastal zone. Various formulations of the ATW exist. A common feature of the ATW models is that the bottom stress is assumed to be proportional to a velocity. Another assumption is that only the along-isobath component of bottom friction is dynamically relevant, while the bottom topography is simplified to be a plane sloping in one direction (Figure 1). The model equations can then be combined into a parabolic equation for a single variable which, for a constant bottom slope, is an analog of the one-dimensional equation for heat conduction. A general, nondimensional form of the equation for a variable �� is

where *x* and *y* are the cross- and along-isobath coordinates, respectively. Negative of *y* plays the role of time in the heat conduction analogy, while the term *Q* is a “source” function depending on the problem at hand. For instance, Csanady's original model resulted in a homogeneous (*Q* = 0) equation for the surface elevation. The author also considered the problem of freshwater influx at the shore, in which a nonhomogeneous term (*Q* ≠ 0) appears in the governing equation [*Csanady*, 1978]. A nonhomogeneous term also appears in the governing equation of other ATW models for flow in a baroclinic ocean. It appears, for instance, in an equation for the along-isobath component of the bottom geostrophic velocity, *v*_{gb}, derived by *Shaw and Csanady* [1983]. The equation for *v*_{gb} was recently used by *Schlichtholz* [2002] to interpret the bottom geostrophic flow over the continental slope in the East Greenland Current in Fram Strait (EGCFS) using hydrographic data from summer 1984 (MIZEX 84 data) and an inverse model based on these data [*Schlichtholz and Houssais*, 1999a].

[3] The southward flow in the EGCFS (Figure 2) is an important element of the current system in the Arctic Mediterranean. Not only it evacuates sea ice and fresh surface polar water from the Arctic Ocean, but it is also a means by which intermediate and deep waters from that ocean can get to the Nordic Seas [e.g., *Aagaard et al.*, 1985; *Rudels et al.*, 1999]. An outflow of these waters occurs along the East Greenland Slope. In addition to water masses advected from the Arctic Ocean along the continental slope, the EGCFS receives some water masses locally in Fram Strait, mainly through westward recirculations of Atlantic and deep waters from the West Spitsbergen Current, and also through injection of surface polar water along the East Greenland Polar Front (Figure 2). Local admixtures gradually change the water mass characteristics along the slope [e.g., *Schlichtholz and Houssais*, 1999b, 2002]. Along-isobath gradients of density are present in the EGCFS near the bottom, as shown by *Schlichtholz* [2002], and generally in the whole water column, as demonstrated by *Schlichtholz and Houssais* [1999c] using distributions of potential energy calculated from the MIZEX 84 data. The along-isobath density gradients are dynamically important since they do not only determine the vertical shear of the cross-isobath component of the geostrophic flow, but also constitute a driving agent for the barotropic flow. The along-isobath variations of the bottom density appear in a formula for the divergence of the bottom geostrophic flow derived by *Shaw and Csanady* [1983]. The formula, when combined with the ATW vorticity balance, gives rise to the “source” term in equation (1) for �� = *v*_{gb}. On the other hand, the along-isobath variations of potential energy appear in the famous JEBAR (joint effect of baroclinicity and relief) term in the vorticity balance for the net flow. The JEBAR effect was introduced to oceanography by *Sarkisyan and Ivanov* [1971] and interpreted in terms of a cross-isobath net baroclinic flow by *Mertz and Wright* [1992]. Its diagnosis from the MIZEX 84 data gave rise to an analytical model of the EGCFS in which the JEBAR term was balanced by a damping term due to either bottom or internal friction [*Schlichtholz and Houssais*, 1999c]. That model was the first attempt to explain the barotropic flow in the EGCFS as resulting from local baroclinic influences over a sloping bottom. The subsequent study of *Schlichtholz* [2002] made it clear that, on the assumption of geostrophy, the bottom flow in the current should be maintained by the effect of along-isobath variations of the bottom density. The effect can be referred to as JEBAR_{b} (joint effect of bottom baroclinicity and relief) in order to stress the fact that it involves baroclinicity at the ocean bottom instead of a total (depth-integrated) baroclinicity.

[4] The present study is intended to give further insight into the dynamics of the EGCFS and tackles, after an introduction of basic equations in section 2, with four problems. The first problem concerns the validity of the ATW balance which is checked in section 3 against observations reported in the literature. The second problem concerns the persistence of the JEBAR_{b}. Till now only the importance of that effect for maintaining the flow in summer 1984 has been evidenced. In section 4, the effect is quantified using climatological data. A short discussion of a relationship between the along-isobath bottom density variations and the distribution of the baroclinic transport is included in that section. Errors of the climatological fields are discussed in Appendix A. The third problem is whether an analytical solution to equation (1) can grasp main features of the bottom flow in the EGCFS. An approximate solution for *v*_{gb} when *Q* = *const*, analogous to the solution for the surface elevation in Csanady's problem of freshwater influx at the shore, was mentioned by *Schlichtholz* [2002]. That solution is a part of a solution in a domain which is semi-infinite in both *x* and *y* [*Csanady*, 1978]. Here, in section 5, exact solutions are obtained in a domain bounded in *x* (Figure 1). The fourth problem, discussed in section 6, concerns a relationship between the JEBAR_{b} and JEBAR in general, and in the EGCFS in particular.