Single-layer barotropic results for three different values of the background shear. Parameters of the “double-tanh” model (35): depth φ = 0.1, h₁( − ∞) = 3.77, ξ = 0.1. Growth rates shown as a function of varying the relative position of the PV jump, Δ, and variations of the asymptotic height as x → ∞, i.e. h₁(∞). Instability growth rates in units of 1/(εΩ₀) (with α = 1). Instability boundaries shown as shaded region. Top figure: q = 1.5 (Keplerian). Middle and bottom figures: q = 0.5, 0.25, respectively. Vertical line designates symmetric step profiles. As the shear decreases, the corresponding growth rates decreases, but the range of possible unstable values of Δ increases.