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Linear stability of inviscid, parallel, and stably stratified shear flow isstudied under the assumption of smooth strictly monotonic profiles of shearflow and density, so that the local Richardson number is positive everywhere.The marginally unstable modes are systematically found by solving aone-parameter family of regular Sturm-Liouville problems, which can determinethe stability boundaries more efficiently than solving the Taylor-Goldsteinequation directly. By arguing for the non-existence of a marginally unstablemode, we derive new sufficient conditions for stability, which generalize theRayleigh-Fj{\o}rtoft criterion for unstratified shear flows.

Stability Boundaries and Sufficient Stability Conditions for Stably Stratified, Monotonic Shear Flows