Question

If νt is the turbulent kinematic viscosity, lm is the mixing length and U is the mean flow velocity in the x-direction, which of these gives the Prandtl mixing length model equation?

(a) \(ν_t =l_m^2 \Big|\frac{∂U}{∂x}\Big|\)

(b) \(ν_t =l_m^2 \Big|\frac{∂U}{∂y}\Big|\)

(c) \(ν_t =l_m \Big|\frac{∂U}{∂y}\Big|\)

(d) \(ν_t =l_m^2 \Big|\frac{∂U}{∂x}\Big|\)

This question was posed to me in homework.

Enquiry is from Mixing Length Turbulence Model in section Turbulence Modelling of Computational Fluid Dynamics

Answer 1

Right option is (b) \(ν_t =l_m^2 \Big|\frac{∂U}{∂y}\Big|\)

To elaborate: Prandtl mixing length model is an attempt to give the transport of momentum in terms of Reynolds stresses. \(ν_t =l_m^2 \Big|\frac{∂U}{∂y}\Big|\) gives the Prandtl mixing length model.