CMS-Flow:Subgrid Turbulence Model

Subgrid Turbulence Model

In CMS-Flow eddy viscosity is calculated as

     ${\nu }_t=(1-{\theta }_m){\nu }_c+{\theta }_m{\nu }_w$  

where ${\theta }_m$ is weighting factor equal to ${\theta }_m=(H_s/h{)}^3$ in which $H_s$ is the significant wave height and ${\nu }_c$ and ${\nu }_w$ are the current- and wave-related eddy viscosity components respectively. The wave contribution is included using the equation of Kraus and Larson (1991)

     ${\nu }_w=\mathrm{\Lambda }{u}_{w}h$

where $\mathrm{\Lambda }$ is an empirical coefficient (default is 0.5), and $u_w$ is the wave bottom orbital velocity and $h$ is the water depth. The current-related eddy viscosity is calculated as a function of the flow gradients, and the bottom shear stress

     ${\nu }_c={\nu }_0+\sqrt{(c_0{u}_{*}h{)}^2+(l_h^2|S|{)}^2}$

where ${\nu }_0$ is a base value approximately equal to the kinematic viscosity, $c_0$ is an empirical coefficient, $l_h$ is the subgrid mixing length, and $|S|$ is equal to

     $|S|=\sqrt{2(\frac{\partial U}{\partial x}{)}^2+2(\frac{\partial V}{\partial y}{)}^2+(\frac{\partial U}{\partial y}+\frac{\partial V}{\partial x}{)}^2}$

The mixing length is calculated here as

     $l_h=c_{sm}\text{<mrow data-mjx-texclass="ORD">min</mrow>}(\sqrt{\mathrm{\Delta }x\mathrm{\Delta }y},h)$ 

where $c_{sm}$ is an empirical coefficient (Smagorinsky coefficient).

---

References

LARSON, M.; HANSON, H., and KRAUS, N. C., 2003. Numerical modeling of beach topography change. Advances in Coastal Modeling, V.C. Lakhan (eds.), Elsevier Oceanography Series, 67, Amsterdam, The Netherlands, 337-365.

---

CMS-Flow