On interfacial instability as a cause of transverse subcritical bed forms

Abstract

Recent experimental results suggest there are at least two distinct bed form initiation processes. Bed forms may be generated from local bed defects that are propagated down and across stream by flow separation processes when sediment transport is patchy and sporadic. Alternatively, bed form development may occur over the whole bed at once when sediment transport is general and widespread. Herein, we critically test a simple model for this latter bed form initiation mode that was originally presented by H.‐K. Liu in 1957 but not tested because of the complex nature of the measurements required. The theory is based on the idea that a moving sand bed might be likened to a dense fluid and that a hydrodynamic instability develops at the interface between the sediment transport layer and the near‐bed fluid, leading to the organization of the transport system into laterally extended, discrete bed forms. Our predicted initial bed form lengths are within 10% of the lengths observed in a series of flume experiments, suggesting that transverse waveforms on sand beds sheared by unidirectional currents can be initiated as an interfacial hydrodynamic instability of Kelvin‐Helmholtz type when the current is sufficiently vigorous to produce general sediment movement, that is, to create a sediment transport layer that acts as a pseudofluid with density composed of solid and fluid components.

Numerical simulation of sand waves in a turbulent open channel flow

“…The growth stage is mostly associated with a transition from 2D spanwise features to less regular and larger size 3D bedforms, as discussed by Venditti & Church (2005) and Venditti et al (2006). Once the sand waves reach their 3D stage, they mainly migrate with the main flow, only slightly increasing in size.…”

“…Starting from the flat bed condition and during the first 160 s of the experimental run, Venditti & Church (2005) (see also Venditti et al 2006) reported the emergence of various, progressively larger and more complex features on the bed. In the sequence they appeared in the experiment, these include: (i) spontaneously occurring cross-hatch patterns over the entire bed surface; (ii) chevron-shaped features at the nodes of the cross-hatch; (iii) incipient sand wave crestlines arising as the result of chevron migration; (iv) quasi-2D sand waves forming as crestlines become more organized in the spanwise direction; (v) growth of sand waves in length and amplitude; and (vi) transition to fully grown 2D bed features.…”

“…Raudkivi 1966;Allen 1968Allen , 1971Hino 1968;van Rijn 1984van Rijn , 1993Gyr & Schmid 1989;Khelifa & Ouellet 2000;Venditti & Bennett 2000;Hansen et al 2001;Venditti & Church 2005;Venditti et al 2005aVenditti et al , 2006Raudkivi 2007;Mazumder et al 2009;Dreano et al 2010;Sarkar & Dey 2010). Theoretical approaches, relying on linear stability theory, have also contributed important insights into the mechanisms that destabilize an initially flat mobile bed and give rise to sand waves.…”

Predicting bedforms and primary current stratification in cohesive mixtures of mud and sand

“…In sedimentary geology, as well as in hydraulic engineering, the characterization of these relationships for non-cohesive silt, sand and gravel is based on descriptive and empirical methods, because the physical processes responsible for the initiation, growth and stability of bedforms are still not fully known. Yet numerous scientific papers have investigated bed defects and wavelets that constitute the first expression of bedform development on a flat sediment bed, and their relation to coherent structures in the near-bed flow (Kennedy 1964(Kennedy , 1969Allen 1968Allen , 1979Southard & Dingler 1971;Williams & Kemp 1971;Kaneko & Honji 1979;Richards 1980;Kobayashi & Madsen 1985;Best 1992Best , 1993Best , 1996Rubin 1992;Baas 1994;Nelson et al 1995;Coleman & Melville 1996;Coleman et al 2003;Colombini 2004;Carling et al 2005;Venditti et al 2005Venditti et al , 2006Wierschem et al 2008;Chou & Fringer 2010;Fourrière et al 2010;Coleman & Nikora 2011;Bose & Dey 2012;Charru et al 2013;Perillo et al 2014a).…”

Validation of a Numerical Model for Flow and Bedform Dynamics

“…Venditti et al 15) ascribed the initiation process to a Kelvin-Helmholtz instability and reintroduced a simple quantitative model for hydrodynamic instability to explain bedform initiation and validated with the results of their experiments. They proposed a relationship for interfacial instability to determine the initial wavelength at which the interface becomes unstable.…”