A roughness-dependent model

(Difference between revisions)

Revision as of 15:07, 19 June 2007

$\nu _t = C_{\mu} {{k^2 } \over \varepsilon }$

(1)

where: $C_{\mu} = 0.09$

$\nu _t = k^{{1 \over 2}} l$

(2)

$\nu _t(y) = {C_{\mu}}^{{1 \over 4}} l_m(y) k^{{1 \over 2}}(y)$

(3)

$l_m$ is the mixing length.

Algebraic model for the turbulent kinetic Energy:

$k^{{1 \over 2}}(y) = {1 \over {C_{\mu}}^{{1 \over 4}}} u_\tau e^{\frac{-y}{A}}$

(4)

$u_\tau$ is the shear velocity

Algebraic model for the mixing length, based on (4) :

$l_m(y) = \kappa \left( A - \left(A - y_0\right) e^{\frac{-(y-y_0)}{A}} \right)$

(5)

$\kappa = 0.4$ , $y_0$ is the hydrodynamic roughness

the algebraic eddy viscosity model is therefore:

$\nu _t(y) = \kappa \left( A - \left(A - y_0\right) e^{\frac{-(y-y_0)}{A}} \right) u_\tau e^{\frac{-y}{A}}$

(6)

Absi, R. (2006), "A roughness and time dependent mixing length equation", Journal of Hydraulic, Coastal and Environmental Engineering, Japan Society of Civil Engineers, (Doboku Gakkai Ronbunshuu B), Vol. 62, No. 4, pp.437-446.

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 <math>l_m</math> is the mixing length.
-where:
+Algebraic model for the turbulent kinetic Energy:
 <table width="70%"><tr><td>
 <math>
@@ Line 27: / Line 27: @@
 <math>u_\tau </math> is the shear velocity
-and:
+Algebraic model for the mixing length, based on (4) :
 <table width="70%"><tr><td>
 <math>
@@ Line 34: / Line 34: @@
 <math>\kappa = 0.4</math>, <math>y_0</math> is the hydrodynamic roughness
-therefore:
+the algebraic eddy viscosity model is therefore:
 <table width="70%"><tr><td>
 <math>