The existence of the Kelvin-Helmholtz instability was first discovered by German physiologist and physicist Hermann von Helmholtz in 1868. Helmholtz identified that "every perfect geometrically sharp edge by which a fluid flows must tear it asunder and establish a surface of separation". Following that work, in 1871, collaborator William Thomson (later Lord Kelvin), developed a mathematical solution of linear instability whilst attempting to model the formation of ocean wind waves.
Throughout the early 20th Century, the ideas of Kelvin-Helmholtz instabilities were applied to a range of stratified fluid applications. In the early 1920s, Lewis Fry Richardson developed the concept that such shear instability would only form where shear overcame static stability due to stratification, encapsulated in the Richardson Number. 
Geophysical observations of the Kelvin-Helmholtz instability were made through the late 1960s/early 1970s, for clouds, and later the ocean.