Boussinesq eddy viscosity assumption
In 1877 Boussinesq postulated that the momentum transfer caused by turbulent eddies can be modeled with an eddy viscosity. This is in analogy with how the momentum transfer caused by the molecular motion in a gas can be described by a molecular viscosity. The Boussinesq assumption states that the Reynolds stress tensor, , is proportional to the mean strain rate tensor, , and can be written in the following way, for an incompressible flow :
Where is a scalar property called the eddy viscosity. The same equation can be written more explicitly as:
The Boussinesq eddy viscosity assumption is also often called the Boussinesq hypothesis or the Boussinesq approximation.
Boussinesq, J. (1877), "Théorie de l’Écoulement Tourbillant", Mem. Présentés par Divers Savants Acad. Sci. Inst. Fr., Vol. 23, pp. 46-50.