The Taylor–Goldstein equation is a fundamental equation in fluid dynamics and hydrodynamic stability theory, particularly in the study of parallel flows and stability analyses of shear flows. It derives from the linear stability analysis of a basic state in a fluid that is affected by small disturbances.
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The Taylor–Goldstein equation governs linear two-dimensional disturbances of an inviscid, vertically sheared, stably stratified parallel flow. For horizontal phase velocity , base velocity , buoyancy frequency , and horizontal wavenumber ,