Marginally unstable Holmboe modes for smooth density and velocity profiles are studied. For a large family of flows and stratification that exhibit Holmboe instability, it is shown that the modes with phase velocity equal to the maximum or the minimum velocity of the shear are marginally unstable. This allows us to determine the critical value of the control parameter R expressing the ratio of the velocity variation length scale to the density variation length scale above which Holmboe… CONTINUE READING