On interfacial instability as a cause of transverse subcritical bed forms

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1 On interfacial instability as a cause of transverse subcritical bed forms Venditti, J.G., Church, M. and Bennett, S. J. (2006) Water Resources Research, 42

2 Two main questions 1. By what processes are bed forms initiated? 2. What is their ultimate stable configuration? Some theories Formation and propagation of a bed defect Kinematic wave formation Amplification of a perturbation Generation of an interfacial instability at the watersediment interface

Interfacial instability mechanism A Kelvin-Helmholtz type instability develops along the interface between the active bed-load layer ( slow but dense) and the viscous sublayer of the overlying fluid

3 Interfacial instability mechanism A Kelvin-Helmholtz type instability develops along the interface between the active bed-load layer ( slow but dense) and the viscous sublayer of the overlying fluid ( fast but less dense) This causes periodic streamwise variations in velocity along the bed, creating internal waveforms on the interface Bedforms are initiated by this fluid mechanical instability, while they may grow by wave amplification

4 A simple model Liu (1957): an interface between two fluids will be stable if Where L is a system length scale Rearranging this gives the wavelength at which the interface is unstable:

5 Experiment Venditti et al. (2006) test this theory through a series of flume experiments under subcritical, fully turbulent conditions with narrowly graded sand (D50 = 0.5 mm) Monitored bed development with high resolution video camera looking down on the flume Bed form height, length and migration rate monitored with two acoustic echo sounders (gives an estimate of transport rate) Transport rate also measured with miniature Helley-Smith sampler Grain velocities at the surface of the active layer estimated by tracking black seed particles Depth of active bed load layer estimated by several methods all give depths on order of 1 mm used with transport rate from echo sounders to calculate density of active layer (see paper for details)

6 Observations At the two flows below/near critical Shields stress, sediment transport was patchy and bed forms only developed if an artificial bed defect was introduced At the three flows above critical Shields stress, sediment transport was continuous over the whole flume and bed forms initiated simultaneously everywhere on the bed

7 Instantaneous bed form initiation Initial flat bed Cross-hatch pattern Chevron scallops at cross-hatch nodes migrate to form incipient crest lines Crestlines straighten into 2D features

8 Analysis The observed values of bed form wavelength were compared with those predicted based on the simple interfacial instability model Predictions were made using combinations of: u 1 = flow velocity measured at 5.0 mm above the bed u 1 = estimate of flow velocity at 2.5 mm above the bed based on a logarithmic profile u 2 = average particle velocity at the surface of the active layer (u p ) from particle tracking measurements u 2 = depth-averaged particle velocity (given by u p /2) The error associated with these predictions ranged from 37% to 47%, compared with an error of 3.5% to 4.4% for the observed bedform wavelengths

9 Analysis Despite substantial error in prediction, the best predicted values fall within 10% of the observed values (for flow velocity measurements at 2.5 mm above the bed and depth-averaged particle velocity up/2)

10 Conclusions and Discussion There are at least two bed form initiation processes: propagation and amplification of bed defects near or below critical Shields stress and instantaneous bed form initiation well above critical Shields stress The results of this experiment are consistent with the idea that bed forms can be produced by an interfacial hydrodynamic instability (K-H type) No need for a turbulent mechanism! Instability creates local erosion and deposition, producing features that scale with the height of the active bed load layer and the viscous sublayer.but once produced, the bed forms alter the structure of the overlying flow and grow out of their original K-H scaling to scale with boundary layer thickness

Aqueous and Aeolian Bedforms

Aqueous and Aeolian Bedforms 1 Further reading & review articles R.A. Bagnold, 1941, The physics of blown sand and desert dunes Charru et al., 2013, Sand ripples and dunes, Ann. Review of Fluid Mech. 2