Eddy Viscosity: Difference between revisions
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<math>v_c = c_{v}u_{*}h </math> (2-23) | <math>v_c = c_{v}u_{*}h </math> (2-23) | ||
where c<sub>v</sub> is approximately equal to <math>\kappa/6=0.0667. | where c<sub>v</sub> is approximately equal to <math>\kappa/6=0.0667.</math> | ||
Subgrid Model | Subgrid Model | ||
The third option for calculating the current-related eddy viscosity, ν<sub>c</sub> , is the subgrid turbulence model given by | The third option for calculating the current-related eddy viscosity, ν<sub>c</sub> , is the subgrid turbulence model given by | ||
<math>v_c = c_{v}u_{*}h + (c_s \Delta)^2 \mid \bar{S} | <math>v_c = c_{v} u_{*} h + (c_s \Delta)^2 \mid\bar{S}\mid </math> (2-24) | ||
in which | |||
c<sub>v</sub> = vertical shear coefficient [-] | |||
c<sub>h</sub> = horizontal shear coefficient [-] | |||
<math>\mid\bar{S}\mid</math> = magnitude of the deformation (strain rate) tensor <math> e_{ij} = \left(\sqrt {2e_{ij}e_{ij}} \right) </math> | |||
Revision as of 20:24, 18 July 2014
The term eddy viscosity arises from the fact that small-scale vortices or eddies on the order of the grid cell size are not resolved and only the large-scale flow is simulated. The eddy viscosity is intended to simulate the dissipation of energy at smaller scales than the model can simulate. In the nearshore environment, large mixing or turbulence occurs due to waves, wind, bottom shear, and strong horizontal gradients; and therefore the eddy viscosity is an important aspect which can have a large influence on the calculated flow field and resulting sediment transport. In CMS-Flow, the total eddy viscosity, νt , is equal to the sum of three parts: 1) a base value ν0, 2) the current-related eddy viscosity νc, and 3) the wave-related eddy viscosity νw and is defined as,
(2-21)
The base value (ν0) is approximately equal to the kinematic eddy viscosity (~1×10-6 m2/s), but may be changed by user. The other two components (νc and νw) are described in the sections below.
Current-Related Eddy Viscosity Component
There are four algebraic models for the current-related eddy viscosity: 1) Falconer Equation, 2) depth-averaged parabolic, 3) subgrid, and 4) mix-ing-length. The default turbulence model is the subgrid model, but may be changed in the user.
Falconer Equation
The Falconer (1980) equation was the default method applied in earlier version of CMS (Militello et al. 2004) for the current-related eddy viscosity. The equation is given by
(2-22)
where cb is the bottom friction coefficient, U is the depth-averaged current velocity magnitude, and h is the total water depth.
Depth-averaged Parabolic Model
The second option for the current-related eddy viscosity is the depth-averaged parabolic model given by
(2-23)
where cv is approximately equal to
Subgrid Model The third option for calculating the current-related eddy viscosity, νc , is the subgrid turbulence model given by
(2-24)
in which
cv = vertical shear coefficient [-]
ch = horizontal shear coefficient [-]
= magnitude of the deformation (strain rate) tensor
