National Center or Earth-surace Dynamics: Summary o Lectures on Transport o Non-Cohesive Sediment What is Morphodynamics? Sediment Properties Modes o Transport o Sediment Equations or Conservation o Bed Sediment Overview o Fluid Dynamics Threshold o Motion Skin Friction and Form Drag Relations or Bed Load Transport Relations or Entrainment o Bed Sediment into Suspension Formulation or Suspended Sediment Sediment Transport in Wave Boundary Layers Formulation or Wave-Current Boundary Layers
National Center or Earth-surace Dynamics: WHAT IS MORPHODYNAMICS? THE ORIGINS OF MORPHODYNAMICS:DUNE ASYMMETRY Felix Maria Exner, an Austrian physicist, asked the ollowing question circa 90. Why do river dunes have gentle stoss (upstream) aces and steep lee (downstream) aces? Looking upstream: Lab (SAFL)
National Center or Earth-surace Dynamics: MORE DUNES: NOTE THE ASYMMETRY Looking upstream: Lab (H. Ikeda) Looking downstream: Field (Amazon basin)
National Center or Earth-surace Dynamics: THE PARAMETERS x streamwise distance [L] t time [T] η bed elevation [L] q t volume total sediment transport rate per unit stream width [L /T] λ p bed porosity [] g acceleration o gravity [L/T ] H low depth U depth-averaged low velocity [L/T] C bed riction coeicient [] The low changes the bed The bed changes the low
National Center or Earth-surace Dynamics: THE STAGE Enxer equation o bed sediment continuity η qt ( λp ) t x Sediment transport relation q t q t (U) FELIX EXNER WAS THE FIRST MORPHODYNAMICIST St. Venant shallow water equations H UH + 0 t x UH U H + t x gh H x gh η x C U
National Center or Earth-surace Dynamics: EXNER REDUCED THE PROBLEM TO A PROBLEM OF NONLINEAR WAVE DYNAMICS He ound. Dunes like Froude-subcritical low.. Dunes migrate downstream as mass waves. 3. Dunes are nonlinear waves: migration speed changes with elev, c c(η) 4. In particular, wave speed increases with elevation 5. Voilà, the asymmetry evolves on its own!
National Center or Earth-surace Dynamics: MORPHODYNAMICS: EXPLAIN HOW WATER AND SEDIMENT INTERACT TO MAKE THESE BEAUTIFUL PATTERNS
National Center or Earth-surace Dynamics: SEDIMENT PROPERTIES Rio Cordon, Italy ρ s density o sediment [ML -3 ] commonly.5 ~.8 g/cm 3 quartz:.65 g/cm 3 ρ density o water [ML -3 ], ~ g/cm 3 R ρ s /ρ -, [], ~.65 (submerged speciic gravity) D characteristic grain size [L], mm v s all velocity o sediment [LT - ]
National Center or Earth-surace Dynamics: SEDIMENT SIZE: LOGARITHMIC PHI AND PSI SCALES D ψ φ ψ φ l (D) n ln(d) ln() D (mm) ψ φ 4 - - 0 0 0.5-0.5-0.5-3 3
National Center or Earth-surace Dynamics: SEDIMENT SIZE RANGES Type D (mm) ψ φ Notes Clay < 0.00 < -9 > 9 Usually cohesive Silt 0.00 ~ 0.065-9 ~ -4 4 ~ 9 Cohesive ~ noncohesive Sand 0.065 ~ -4 ~ - ~ 4 Non-cohesive Gravel ~ 64 ~ 6-6 ~ - Cobbles 64 ~ 56 6 ~ 8-8 ~ -6 Boulders > 56 > 8 < -8 Non-cohesive coastal morphodynamics is mostly about sand
National Center or Earth-surace Dynamics: 0.9 SEDIMENT GRAIN SIZE DISTRIBUTIONS Sample Grain Size Distribution Characterize grain size distribution in terms o N+ sizes D b,i such that,i denotes the raction in the sample that is iner than size D b,i 0.8 Fraction Finer 0.7 0.6 0.5 0.4 0.3 0. 0. 0,4 D b,4 0.0 0. 0 Grain Size mm Use logarithmic scale! i D b,i mm,i 0.035 0.00 0.065 0.03 3 0.05 0.00 4 0.5 0.4 5 0.5 0.834 6 0.970 7 0.990 8 4.000
National Center or Earth-surace Dynamics: Fraction Finer 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0. 0 CHARACTERISTIC SIZES BASED ON PERCENT FINER Sample Grain Size Distribution D 50 D 90 0.0 0. 0 Grain Size mm D 50 0.86 mm; D 90 0.700 mm D x is size such that x percent o the sample is iner than D x Examples: D 50 median size D 90 ~ roughness height To ind D x (e.g. D 50 ) ind i such that ψ D x x ψ x 00,i,i+ b,i ψ x + ψ Then b,i+,i+ ψ,i b,i x 00,i
National Center or Earth-surace Dynamics: STATISTICAL CHARACTERISTICS OF SIZE DISTRIBUTION Sample Grain Size Distribution N+ bounds deines N grain size ranges. The ith grain size range is deined by (D b,i, D b,i+ ) and (,i,,i+ ) Fraction Finer 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 4 ψ D i i i ( ψ ψ ) ( D D ) / b,i,i + b,i b,i+,i b,i+ 0. 0 0.0 0. 0 Grain Size mm 4 0.444; D 4 0.354 mm ψ I (D i ) characteristic size o ith grain size range i raction o sample in ith grain size range
National Center or Earth-surace Dynamics: STATISTICAL CHARACTERISTICS OF SIZE DISTRIBUTION Fraction Finer 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0. Sample Grain Size Distribution ψ mean grain size on psi scale σ standard deviation on psi scale ψ σ D σ g g N i N i ψ σ ψ i i ( ψ ψ) i i 0 0.0 0. 0 Grain Size mm D g 0.96 mm, σ g.7 D g geometric mean size σ g geometric standard deviation ( ) Sediment is well sorted i σ g <.6
National Center or Earth-surace Dynamics: SEDIMENT FALL VELOCITY IN STILL WATER Assume a spherical particle with diameter D The downstream impelling orce o gravity F g is: F D F g 4 D Fg πρrg 3 The resistive drag orce is D FD πρcd v s, c 3 D where ν is the kinematic viscosity o the water and c D is speciied by the empirical drag curve or spheres c D ( Re ) vp, Re vp v sd ν Condition or equilibrium: F g F D R / [ ] 3c D 4 ( Re vp ) where R v s RgD
R [ 4 / 3c ] D(Rep ) National Center or Earth-surace Dynamics: SEDIMENT FALL VELOCITY IN STILL WATER Untangle the relation F D 4 / v R R s [ ] where and 3c ( Re ) RgD D vp Re vp v s D ν Fg v D v RgD D Re where p ν RgD ν s d Re vp R Re p RgD D ν Reduce to R R (Re p ) Relation o Dietrich (98): R b exp { b 4 [ ln ( Re p )] + b 3 + b ln( Re 5 p [ ln ( Re ) b p )] 3 4 [ ln( Re Original relation also includes correction or shape } p )] b.89394 b 0.9596 b 3 0.056835 b 4 0.0089 b 5 0.00045
R [ 4 / 3c ] D(Rep ) National Center or Earth-surace Dynamics: SOME SAMPLE CALCULATIONS OF SEDIMENT FALL VELOCITY (Dietrich Relation) g 9.8 ms - R.65 (quartz) ν.00x0-6 m s - (water at 0 deg Celsius) ρ 000 kgm -3 (water) D, mm v s, cm/s 0.065 0.330 0.5.08 0.5 3.04 0.5 7.40 5.5 8.3
R [ 4 / 3c ] D(Rep ) National Center or Earth-surace Dynamics: MODES OF TRANSPORT OF SEDIMENT Bed material load is that part o the sediment load that exchanges with the bed (and thus contributes to morphodynamics). Wash load is transported through without exchange with the bed. In rivers, material iner than 0.065 mm (silt and clay) is oten approximated as wash load. Bed material load is urther subdivided into bedload and suspended load. Bedload: sliding, rolling or saltating just above bed role o turbulence is indirect Suspended load: eels direct dispersive eect o eddies may be wated high into the water column
R [ 4 / 3c ] D(Rep ) National Center or Earth-surace Dynamics: TRANSPORT DOMINATED BY BEDLOAD (Delta progradation at SAFL: M. Kleinhans) video clip
R [ 4 / 3c ] D(Rep ) National Center or Earth-surace Dynamics: TRANSPORT DOMINATED BY BEDLOAD (courtesy Vicenzo D Agostino) video clip
National Center or Earth-surace Dynamics: TRANSPORT DOMINATED BY SUSPENDED LOAD (Sand-mud turbidity current at SAFL: J. Marr) video clip