The random eddy motion of groups of particles resembles the random motion of molecules in a gas—colliding with each other after traveling a certain distance and exchanging momentum in the process. Therefore, momentum transport by eddies in turbulent flows is analogous to the molecular momentum diffusion. In many of the simpler turbulence models, turbulent shear stress is expressed in an analogous manner as suggested by the French mathematician Joseph Boussinesq (1842–1929) in 1877 as

$τ_{turb}=-ρ(v^{'} ) ̅(u^{'} ) ̅=μ_t \frac{∂u ̅}{∂y}$

Where, $μ_t$ is the eddy viscosity or turbulent viscosity which accounts for momentum transport by turbulent eddies. Then the total shear stress can be expressed conveniently as

$τ_total=(μ+μ_t ) \frac{∂u ̅}{∂y}=ρ(v+v_t ) \frac{∂u ̅}{∂y}$

Where $v_t=μ_t⁄ρ$ the kinematic eddy viscosity or kinematic turbulent viscosity is (also called the eddy diffusivity of momentum). The concept of eddy viscosity is very appealing, but it is of no practical use unless its value can be determined. In other words, eddy viscosity must be modeled as a function of the average flow variables; we call this eddy viscosity closure.