Explicit nonlinear constitutive relation
An explicit nonlinear constitutive relation for the Reynolds stresses represents an explicitly-postulated expansion over the linear Boussinesq hypothesis.
One of such explicit and nonlinear expansion over the Boussinesq hypothesis, as proposed by [Wallin & Johansson (2000)], is given by
Note that the terms in the first line are exactly the linear relation as expressed by the Boussinesq hypothesis.
- Wallin, S., and Johansson, A. V. (2000), "An Explicit Algebraic Reynolds Stress Model for Incompressible and Compressible Turbulent Flows", Journal of Fluid Mechanics, Vol. 403, Jan. 2000, pp. 89–132.