Nonlinear eddy viscosity models

 Turbulence RANS-based turbulence models Linear eddy viscosity models Nonlinear eddy viscosity models Explicit nonlinear constitutive relation v2-f models $\overline{\upsilon^2}-f$ model $\zeta-f$ model Reynolds stress model (RSM) Large eddy simulation (LES) Detached eddy simulation (DES) Direct numerical simulation (DNS) Turbulence near-wall modeling Turbulence free-stream boundary conditions

This is class of turbulence models for the RANS equations in which an eddy viscosity coefficient is used to relate the mean turbulence field to the mean velocity field, however in a nonlinear relationship $- \rho \left\langle u_{i} u_{j} \right\rangle = 2 \, \mu_{t} \, \mathcal{F}_{nl} \left( S_{ij}, \Omega_{ij}, \dots \right)$

where

• $\mathcal{F}_{nl}$ is a nonlinear function possibly dependent on the mean strain and vorticity fields or even other turbulence variable
• $\mu_{t}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
• $S_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}} \right] - \frac{1}{3} \frac{\partial U_{k}}{\partial x_{k}} \delta_{ij}$ is the mean strain rate
• $\Omega_{ij}= \frac{1}{2} \left[ \frac{\partial U_{i}}{\partial x_{j}} - \frac{\partial U_{j}}{\partial x_{i}} \right]$ is the mean vorticity