these are largely manifested in the horizontal plane over most of the water

column. It is expected that the shed vortices will be in approximate similitude

in a geometrically distorted physical model. Experiments conducted to assess

potential turbulence scaling effects in distorted models are discussed in the

following chapter.

Finally, in addition to scale effects related to generation of turbulence, any

mechanism that creates significant vertical velocities or accelerations will be

problematic in a geometrically distorted model. For example, at river bends

centrifugal forces pile water up on the outside of the bend, which creates a lateral

slope in the water surface. The force imbalance results in a cross-channel return

flow toward the inside of the curve along the bottom. The resulting secondary

flow resembles a helix as it moves downstream. In a distorted model the curve

geometry will be tighter and the side slopes will be steeper. The same

phenomenon occurs where flow accelerates as it passes a headland or jetty

causing a lowering of the local water surface.

Similitude requirements are formally determined as before, only this time the

following governing equations are presented in cylindrical coordinates as often

adopted for numerical modeling of flow around river bends. Turbulence terms

and viscous shear stress terms have been omitted from the momentum equations

to focus on the distorted model scale effects associated with flow acceleration at

a river bend.

∂*v*r vr 1 ∂*v*θ ∂*v*z

++

+

=0

(18)

∂*r*

∂*z*

r-direction momentum

2

∂*v*r

∂*v*r vθ ∂*v*r vθ

∂*v*

1 ∂*p*

+ *v*r

+

- + *v*z r = -

(19)

ρ ∂*r*

∂*t*

∂*r*

∂*z*

acceleration terms

pressure term

θ-direction momentum

∂*v*θ

∂*v*

∂*v*

1 ∂*p*

+ *v*r θ + θ θ + r θ + *v*z θ = -

(20)

ρ r ∂θ

∂*t*

∂*r*

∂*z*

acceleration terms

pressure term

32

Chapter 4 Turbulence Scale Effect in Distorted Models

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