1. 1B Clastic Sediments Lecture 28 BEDFORMS IN COHESIONLESS SUBSTRATE Structure of bedforms Formative conditions Unidirectional and Oscillating flows NH 01-2007

2. BURSTS AND SWEEPS Flow streaks in wall region. Spacing of streaks, depends on flow properties: Re * =  u * /  = 100 Re * is boundary Reynolds no. u * = √  0 /  is shear velocity. Burst-sweep process is main creator of turbulence. Inrush of high-velocity sweeps may locally exceed threshold of sediment motion.

3. RIPPLE INITIATION Ripples form when random points of high boundary shear stress (sweeps) cause formation of a pile of grains. Pile of height  v causes flow disturbance ~100  v long downstream, similar to the separation zone behind a ripple. D > 0.7 mm: grains disrupt viscous sublayer and discrete flow disturbances no longer occur. Ripples do not form, bed is plane. Bedform wavelength ~100  v

4. FLOW OVER BEDFORM Ripples and dunes formed under uni- directional flow have shallow upstream or stoss faces, dominated by rolling grains, and steep downstream or lee slopes, dominated by grain avalanching.

5. BEDFORM MIGRATION AND SEDIMENT FLUX Downstream flux of sediment due to bedform migration: where U B is speed of bedform, H is height of bedform,  is porosity of bed material.

6. SEDIMENT FALLOUT Climbing ripples Angle of climb and preservation of stoss and lee side are determined by balance of downstream translation and vertical build up.

7. BEDFORMS PLANFORM AND INTERNAL STRUCTURE Planar cross stratification Trough cross stratification Basic bedform: crescent

8. FLOW OVER BEDFORM Ripples and dunes formed under uni- directional flow have shallow upstream or stoss faces, dominated by rolling grains, and steep downstream or lee slopes, dominated by grain avalanching. Dunes:  ~ 2  h dune height = h/3 to h/D where h is flow depth, and D is grain size. Ripples:height < 4 cm

9. BEDFORMS UNDER SHEAR FLOW On flat bed, resistance to flow is due to boundary roughness (~ grain size): skin friction  0 ~ U a Developing bedforms become main roughness element: form drag With increasing flow velocity :1) bedforms grow, shear stress up. 2) dunes wash out, replaced by flat bed: shear stress down. 3) standing waves and antidunes form: shear stress up. Shear stress bad indicator of state of bed; use flow velocity. Flat bed Antidunes

10. CONTROLS ON BEDFORM: Assumptions: steady and uniform flow, equilibrium bedforms, mean grain size describes bed material. Variables: Grain size D[L] Density of grains  s [ML -3 ] Density of fluid  f [ML -3 ] Viscosity of fluid  [ML -1 T -1 ] Gravitational acceleration g [LT -2 ] Flow depth h[L] Flow velocity U[LT -1 ]

11. BEDFORMS STABILITY FIELDS Flow depth: 0.25 – 0.40 m

12. BEDFORMS STABILITY FIELDS Absence of ripples in course sand: Lack of viscous sublayer over hydraulically rough boundary. Upper plane bed in fine grains: Due to high sediment concentration damping turbulence.

13. FLOW REGIMES Lower flow regime Upper flow regime Hydraulic jump Gravity works to flatten a rough flow: Froude number is dimensionless product expressing balance of inertial and gravitational forces Fr 1: supercritical flow

14. BEDFORMS STABILITY FIELDS; FLOW REGIMES Super critical Upper Sub critical Lower flow regime

15. CONTROLS ON BEDFORM: DIMENSIONAL ANALYSIS Assumptions: steady and uniform flow, equilibrium bedforms, mean grain size describes bed material. Variables: Grain size D[L] Density of grains  s [ML -3 ]exclude Density of fluid  f [ML -3 ]repeat Viscosity of fluid  [ML -1 T -1 ]repeat Gravitational acceleration g [LT -2 ]repeat Flow depth h[L] Flow velocity U[LT -1 ] Dimensionless Products: Experimental set up: Water, quartz sand, variable temperature. constant in temp

16. BEDFORMS STABILITY FIELDS Bedform stability can be represented in 3D plot of standardized flow velocity, flow depth and grain size. Sections through this cube can be viewed. h 10

17. BEDFORMS UNDER OSCILATORY WAVES Controls on bedform:Flow velocity Sediment grain size Wave period Form Index: L/H

18. BEDFORMS UNDER OSCILATORY WAVES