Smyth, W.D., J.N. Moum and J.D. Nash, 2011: “Narrowband, high-frequency oscillations at the equator. Part II: Properties of shear instabilities”, J. Phys. Oceanogr. 41, 412-428. [PDF]
A guide to the relevant theory:
Smyth, W.D. and J.R. Carpenter, 2019, “Instability in Geophysical Flows”, Cambridge University Press. https://www.amazon.com/Instability-Geophysical-Flows-William-Smyth-ebook/dp/B07RP1MC8G/ref=sr_1_1?keywords=smyth+instability&qid=1573683499&sr=8-1
NEW VERSION: Fourier-Galerkin method is faster and more accurate.wave_analysis_FG.m : code to solve demonstration problem
nash_data.txt : observational data for demonstration problem
vTG_FG.m : the main subroutine
BaryL.m : auxiliary subroutine
vTG_FGprep.m : auxiliary subroutine (call first)
Lian, Q., W. D. Smyth, and Z. Liu, 2020: “Numerical Computation of Instabilities and Internal Waves from In Situ Measurements via the Viscous Taylor–Goldstein Problem”. J. Atmos. Oceanic Technol., 37, 759–776, https://doi.org/10.1175/JTECH-D-19-0155.1.
Watch this space for more efficient methods currently in the works.