From AMS Glossary
A parameter used to define the local stability of an inviscid water column to double- diffusive convection.
where tan-1 is the four-quadrant arctangent, α is the coefficient of thermal expansion, β is the coefficient of saline contraction, T is temperature, and S is salinity. If -45° < Tu < 45°, the column is statically stable. If -90° > Tu or Tu > 90°, the column is statically unstable to Rayleigh– Taylor instability. If -90° < Tu < -45°, the column is unstable to diffusive convection. If 45° < Tu < 90°, the column is unstable to salt fingering.