assume β=1. Only for fine particles in very dilute concentrations C=O(0.001) β>1: particles lose correlation with fluid motion as settle through eddies? β<1: centrifugal forces have larger effect on particles than on surrounding fluid? Literature reports values 0.1 to 10 May depend on model equations and boundary conditions Often used as a tunable parameter s t
cm, mesh size M = 5 cm (M/m = 5) Grid porosity 65% = most efficient for reducing secondary flows (Hopfinger and Toly, 1976) Fresh tap water at 20oC seeded with 11um hollow spheres 2 Re fS f=2Hz, S=10cm f=3Hz, S=7cm Solid glass spheres: 70-110μm and 145-205μm
ID) 1,2,4MHz Acoustic Backscatter System (ABS) Suspension of spheres: analytical form function Nortek Vectrino II Acoustic Doppler Profiler (30mm profiles at 100Hz) Only R>90%, Amplitudes>-50dB Phase-space de-spiking (Goring and Nikora, 2002) TURBULENCE
. 0 RgD C C RgD w s Re=2.5 for coarser sediment Ferguson and Church (2004): C1 = 18 C2 = 0.4 for smooth spheres R = 1.65 for quartz in water 1 2 C RgD w s Stokes’ law used for fine sediment D w s Re = 0.45
z z z h c c Model for Concentration Profile Rouse z z h c Replace with the form: ‘reference concentration’ diffusion coefficient
z z h z h c w s s Expression for Sediment Diffusivity Good agreement at high C Worse agreement when C measurements don’t rapidly go to zero
' ' 2 1 w v u k 2 1 5 . 1 5 . 0 2 2 2 1 2 2 1 fz S M C C k C1 = 0.22 C2 = 0.26 DeSilva & Fernando (1992) M=5 S=10 or 7 cm f= 2 or 3Hz Orlins & Gulliver (2003)
t l k C 2 / 3 4 / 3 z l 1 . 0 2 2 2 1 2 C C z M fz S C t 1 . 0 2 1 1 5 . 1 2 1 5 . 1 5 . 0 2 2 2 1 2 2 1 fz S M C C k
sand momentum much more diffusive than sediment s t relatively invariant with depth analytical model gives good approximation = 14705 = 10808 2 Re fS COARSE FINE
>β for smaller particles • Settling of finer grains faster in turbulence than in still water? • Mixing length for finer grains smaller than for the fluid? • β increases with C because of negative feedback? (Lees, 1981; Amoudry et al., 2005) • Stratification effects (which would reduce eddy viscosity and β)
grid turbulence in zero-mean-shear flows • 2 flow conditions and 2 different sized glass spheres • Momentum diffusivity greater than sediment diffusivity (β>1) • Grain-size dependence? • Reynolds number dependence Ongoing work: • Spectral estimation of ε • Greater range of flow conditions and sediment types • Stratification effects • Further investigation of Vectrino II How do these results apply when gradient diffusion not dominant process (e.g. large mixing lengths)?
• Profiles of velocity and concentration • Analytical expressions for sediment diffusivity and turbulent mixing • Vertical profiles of Schmidt number • Discussion of these initial results and ongoing/future work