Sediment Transport Modelling Lab

The Law of the Wall The law of the wall states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the no-slip boundary of the fluid region. This law of the wall was first published by Theodore von Kármán, in It is only technically applicable to parts of the flow that are close to the wall (<20% of the height of the flow), though it is a good approximation for the entire velocity profile of natural streams.

The Law of the Wall u z = ( u * /κ)(ln z/z o ) u * is shear or friction velocity (units of velocity) u * = (τ o /ρ) 0.5 κ is von Karman’s constant (0.4) of mixing length z o is roughness height where u = 0 (I use some online source for antilogs outside excel: log-logarithm-calculator.htmhttp://ncalculators.com/number-conversion/anti- log-logarithm-calculator.htm)

= Boundary shear stress = Shear velocity C d = hydraulic drag coefficient Boundary shear stress can be related to the mean flow velocity, by Relating  b to u Also (H=Flow Depth),

Characterizing Fluid Flow = scale velocity= scale length Froude Number Reynolds Number

Key connections between solid and fluid phase Summary of Relationships between fluid and sediment Experimental Results: Pure Bedload:  b >  cr & w s /u * > 3 Incipient Suspension: 3 > w s /u * > 0.33 Full suspension: w s /u * ≤ 0.33

Estimating Critical Shear Stress (Shield’s Stress) from grain sizes on the bed Particle size / roughness scale (d50) of the bed