The equation is derived by solving a linearized version of the Navier–Stokes equation, in presence of gravity  and a mean density gradient (with gradient-length ), for the perturbation velocity field
where  is the unperturbed or basic flow.  The perturbation velocity has the wave-like solution  (real part understood).   Using this knowledge, and the streamfunction representation
 for the flow, the following dimensional form of the Taylor–Goldstein equation is obtained:
where  denotes the Brunt–Väisälä frequency. The eigenvalue parameter of the problem is . If the imaginary part of the wave speed  is positive, then the flow is unstable, and the small perturbation introduced to the system is amplified in time.
Note that a purely imaginary Brunt–Väisälä frequency  results in a flow which is always unstable. This instability is known as the Rayleigh–Taylor instability.