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Old   October 19, 2009, 12:50
Default Boussinesq Assumption
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Hi all,
I've read that the Boussinesq assumption linearized the relationship between the turbulent stresses and the mean strain rate, so:
u_i*u_j=2/3*k*del_ij - 2*nu_t*S_ij

I've also seen people say that the Boussinesq assumption makes the normal stresses isotropic, so:

My question is where does the second term go? Does the Boussinesq assumption also assume that du/dx = dv/dy = dw/dz = 0?

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Old   October 22, 2009, 08:57
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When the normal stresses are made isotropic, the first term vanishes and you have the linearized equation for the turbulent shear stress (second term)
tau_xy = mu_t * du/dy
where mu_t is the turbulent viscosity
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Old   October 22, 2009, 10:12
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Thanks, but why does the first term vanish? It should vanish if the Kronecker delta is zero, which happens for the off-diagonal terms, not the diagonal terms.

I'm clearly still confused. I appreciate your help!
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Old   October 26, 2009, 06:11
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Expression for Tou ij =2*mue_t*Sij-2/3*k*rho*del_ij;
Sij=2(dui/dxj+duj/dxi)----------Terms here are time averaged.
When i=j; Sii=0 for incompressible flows.
Recollect the time averaged continuity equation.
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