AbstractA modified Eady channel model with oppositely sloping top and bottom Ekman layers is used to examine analytically and numerically the effect of the slope, Δ, with dissipation, δ, on baroclinic flows in linear and nonlinear systems. the spectral wave solution is truncated up to six components.In the linear system, when δ = 0, waves are dispersive and move westward owing to Δ. the maximum value of Δ for which unstable waves may exist, ΔCmax, is equal to the slope of the isentropes of the basic state. Δ exhibits only a weak stabilizing influence on short waves, while exhibiting a strong stabilizing influence on long waves when it exceeds a critical value. When δ ≠ = 0, a small δ has a destabilizing effect on short waves by shifting the short‐wave cut‐off in the shorter wave direction and extending Δcmaxto a larger value. However, the combined effect of Δ and δ strongly stabilizes long waves. the most unstable wavenumber may be shifted to a higher one by increasing Δ, in both inviscid and viscous cases. the relation between the most unstable wavenumber and Δ is similar to some annulus experiments with oppositely sloping boundaries. It is also similar to the relation between the most unstable wavenumber and β in β‐plane models.In a nonlinear system without wave‐wave interaction, Δ stabilizes the flow even for small δ and reduces the domain of vacillation and aperiodic flow regimes, while enlarging the domain of single‐wave steady state. It also qualitatively agrees with the results from β‐plane dissipative systems. Within the single‐wave steady state regime, the preferred nonlinear wavenumber may also be shifted to a higher one by increasing Δ. When wave‐wave interaction is allowed, a variety of flow regimes is observed in four truncated systems. There are single‐wave steady states, multi‐wave steady states where wave dispersion or structural vacillation may occur, multi‐wave vacillation, and aperiodic flows. In contrast to the system without wave‐wave interaction, the domain of vacillation is enlarged. A ‘frequency‐locking’ mechanism is found in multi‐wave steady states, where all three conditions