 Linear stability of a meridional two-layer current

Let $K^2=k^2+l^2$, $A=K^2+F$, $\mathcal{B}=K^2(K^2+2F)$ and use $e^{i(kx+ly-\sigma t)}$. The uniform upper-layer flow $V$ over a resting lower layer has the dispersion relationIts discriminant is $4F^2{\beta }^2{k}^2+\mathcal{B}{K}^2(K^2-2F)l^2{V}^2$. A negative value gives exponential baroclinic instability. This model includes advection across the interface-induced potential-vorticity gradients in a meridional two-layer current.