Counter-gradient flux

From Glossary of Meteorology

counter-gradient flux

A flux of some variable opposite to the mean gradient of that variable.

For example, if temperature decreases upward, then a counter-gradient heat flux would be downward, from cold to hot. While this appears to violate a law of thermodynamics that states heat flows from hot to cold, those laws are found not to be violated when nonlocal motions (air parcels moving across finite distances) are considered. Flux is not caused by, nor related to, the local gradient when coherent structures are present.